SOLUTION: {{{ 3y^2-7y-5=0 }}}

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Question 99891: +3y%5E2-7y-5=0+
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 3%2Ay%5E2-7%2Ay-5=0 ( notice a=3, b=-7, and c=-5)




y+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A3%2A-5+%29%29%2F%282%2A3%29 Plug in a=3, b=-7, and c=-5



y+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A3%2A-5+%29%29%2F%282%2A3%29 Negate -7 to get 7



y+=+%287+%2B-+sqrt%28+49-4%2A3%2A-5+%29%29%2F%282%2A3%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)



y+=+%287+%2B-+sqrt%28+49%2B60+%29%29%2F%282%2A3%29 Multiply -4%2A-5%2A3 to get 60



y+=+%287+%2B-+sqrt%28+109+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



y+=+%287+%2B-+sqrt%28109%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



y+=+%287+%2B-+sqrt%28109%29%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

y+=+%287+%2B+sqrt%28109%29%29%2F6 or y+=+%287+-+sqrt%28109%29%29%2F6


Now break up the fraction


y=%2B7%2F6%2Bsqrt%28109%29%2F6 or y=%2B7%2F6-sqrt%28109%29%2F6


Simplify


y=7+%2F+6%2Bsqrt%28109%29%2F6 or y=7+%2F+6-sqrt%28109%29%2F6


So these expressions approximate to

y=2.90671775148509 or y=-0.573384418151758


So our solutions are:
y=2.90671775148509 or y=-0.573384418151758

Notice when we graph 3%2Ax%5E2-7%2Ax-5 (just replace y with x), we get:



when we use the root finder feature on a calculator, we find that x=2.90671775148509 and x=-0.573384418151758.So this verifies our answer

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
3Y^2-7Y-5=0
USING THE QUADRATIC EQUATION WE GET:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(7+-SQRT[-7^2-4*3*-5])/2*3
X=(7+-SQRT[49+60])/6
X=(7+-SQRT109)/6
X=(7+-10.44)/6
X=(7+10.44)/6
X=17.44/6
X=2.9 ANSWER.
X=(7-10.44)/6
X=-3.44/6
X=.57 ANSWER.