SOLUTION: Hello, I have an algebra 2 question relating to application of the Quadratic formula. The problem is: 2y+3/4y-1=3y-2/3y+2 I have no idea how to do that using the quadratic fo

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello, I have an algebra 2 question relating to application of the Quadratic formula. The problem is: 2y+3/4y-1=3y-2/3y+2 I have no idea how to do that using the quadratic fo      Log On


   

Question 122822This question is from textbook Prentice Hall Algebra 2 with Trigonometry
: Hello, I have an algebra 2 question relating to application of the Quadratic formula.
The problem is: 2y+3/4y-1=3y-2/3y+2
I have no idea how to do that using the quadratic formula.
I appreciate your assistance and thank you in advance. This question is from textbook Prentice Hall Algebra 2 with Trigonometry

Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282y%2B3%29%2F%284y-1%29=%283y-2%29%2F%283y%2B2%29 Start with the given equation



%282y%2B3%29%283y%2B2%29=%283y-2%29%284y-1%29 Cross multiply



6y%5E2%2B13y%2B6=12y%5E2-11y%2B2 Foil



6y%5E2%2B13y%2B6-12y%5E2%2B11y-2=0 Get everything to the left side



-6y%5E2%2B24y%2B4=0 Combine like terms


Let's use the quadratic formula to solve for y:


Starting with the general quadratic

ay%5E2%2Bby%2Bc=0

the general solution using the quadratic equation is:

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve -6%2Ay%5E2%2B24%2Ay%2B4=0 ( notice a=-6, b=24, and c=4)




y+=+%28-24+%2B-+sqrt%28+%2824%29%5E2-4%2A-6%2A4+%29%29%2F%282%2A-6%29 Plug in a=-6, b=24, and c=4



y+=+%28-24+%2B-+sqrt%28+576-4%2A-6%2A4+%29%29%2F%282%2A-6%29 Square 24 to get 576



y+=+%28-24+%2B-+sqrt%28+576%2B96+%29%29%2F%282%2A-6%29 Multiply -4%2A4%2A-6 to get 96



y+=+%28-24+%2B-+sqrt%28+672+%29%29%2F%282%2A-6%29 Combine like terms in the radicand (everything under the square root)



y+=+%28-24+%2B-+4%2Asqrt%2842%29%29%2F%282%2A-6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



y+=+%28-24+%2B-+4%2Asqrt%2842%29%29%2F-12 Multiply 2 and -6 to get -12

So now the expression breaks down into two parts

y+=+%28-24+%2B+4%2Asqrt%2842%29%29%2F-12 or y+=+%28-24+-+4%2Asqrt%2842%29%29%2F-12


Now break up the fraction


y=-24%2F-12%2B4%2Asqrt%2842%29%2F-12 or y=-24%2F-12-4%2Asqrt%2842%29%2F-12


Simplify


y=2-sqrt%2842%29%2F3 or y=2%2Bsqrt%2842%29%2F3


So these expressions approximate to

y=-0.160246899469287 or y=4.16024689946929


So our solutions are:
y=-0.160246899469287 or y=4.16024689946929

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%282y%2B3%29%2F%284y-1%29=%283y-1%29%2F%283y%2B2%29.........first cross multiply

%282y%2B3%29%283y%2B2%29=%283y-1%29%284y-1%29.........

6y%5E2+%2B+4y+%2B+9y+%2B+6+=+12y%5E2+%96+3y+%96+8y+%2B+2……
6y%5E2+%2B+13y+%2B+6+=+12y%5E2+%96+11y+%2B+2……
0+=+12y%5E2+-+6y%5E2+-+13y+%96+11y+-6+%2B+2……
+6y%5E2+-+24y+%96+4+=+0……

+y%5B1%2C2%5D++++=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

+y%5B1%2C2%5D++++=+%2824+%2B-+sqrt%28576+%2B+96%29%29%2F12+
+y%5B1%2C2%5D+++=+%2824+%2B-+sqrt%28672%29%29%2F12+

+y%5B1%5D+++=+%2824+%2B-+25.92%29%2F12+
+y%5B1%5D+++=+%2824+%2B+25.92%29%2F12+
+y%5B1%5D++=++4.16+

+y%5B2%5D++=+%2824+-+25.92%29%2F12+
+y%5B2%5D++=+%28+-+1.92%29%2F12+
y%5B2%5D+=+-0.16+
Check:
If +y%5B1%5D++=++4.16+
%282%284.16+%29%2B3%29%2F%284%284.16+%29-1%29=%283%284.16+%29-1%29%2F%283%284.16+%29%2B2%29.........

%288.32+%2B3%29%2F%2816.64+-1%29=%2812.48+-1%29%2F%2812.48+%2B2%29.........

11.32+%2F15.64+=+10.48+%2F14.48+……
11.32+%2F15.64+=+10.48+%2F14.48+……
0.7237=0.7237