SOLUTION: can someone help me plss before monday? solve the equation. 21. 6x+1/x+20 = 20x+3/3x+7

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Question 473498: can someone help me plss before monday?
solve the equation.
21. 6x+1/x+20 = 20x+3/3x+7
Found 2 solutions by jorel1380, MathLover1:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
6x+1/x+20 = 20x+3/3x+7
(6x+1)(3x+7)=(x+20)(20x+3)
18x2+45x+7=20x2+403x+60
2x2+358x+53=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B358x%2B53+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28358%29%5E2-4%2A2%2A53=127740.

Discriminant d=127740 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-358%2B-sqrt%28+127740+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28358%29%2Bsqrt%28+127740+%29%29%2F2%5C2+=+-0.148167338324839
x%5B2%5D+=+%28-%28358%29-sqrt%28+127740+%29%29%2F2%5C2+=+-178.851832661675

Quadratic expression 2x%5E2%2B358x%2B53 can be factored:
2x%5E2%2B358x%2B53+=+2%28x--0.148167338324839%29%2A%28x--178.851832661675%29
Again, the answer is: -0.148167338324839, -178.851832661675. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B358%2Ax%2B53+%29
..

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%286x%2B1%29%2F%28x%2B20%29+=+%2820x%2B3%29%2F%283x%2B7%29...cross multiply

%286x%2B1%29%283x%2B7%29+=+%2820x%2B3%29%28x%2B20%29

18x%5E2%2B42x%2B3x%2B7=+20x%5E2%2B200x%2B3x%2B60
18x%5E2%2B45x%2B7=+20x%5E2%2B203x%2B60
0=+20x%5E2-18x%5E2%2B203x-45x%2B60-7
2x%5E2%2B158x%2B53=0

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve 2%2Ax%5E2%2B158%2Ax%2B53=0 ( notice a=2, b=158, and c=53)





x+=+%28-158+%2B-+sqrt%28+%28158%29%5E2-4%2A2%2A53+%29%29%2F%282%2A2%29 Plug in a=2, b=158, and c=53




x+=+%28-158+%2B-+sqrt%28+24964-4%2A2%2A53+%29%29%2F%282%2A2%29 Square 158 to get 24964




x+=+%28-158+%2B-+sqrt%28+24964%2B-424+%29%29%2F%282%2A2%29 Multiply -4%2A53%2A2 to get -424




x+=+%28-158+%2B-+sqrt%28+24540+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-158+%2B-+2%2Asqrt%286135%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-158+%2B-+2%2Asqrt%286135%29%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%28-158+%2B+2%2Asqrt%286135%29%29%2F4 or x+=+%28-158+-+2%2Asqrt%286135%29%29%2F4



Now break up the fraction



x=-158%2F4%2B2%2Asqrt%286135%29%2F4 or x=-158%2F4-2%2Asqrt%286135%29%2F4



Simplify



x=-79%2F2%2Bsqrt%286135%29%2F2 or x=-79%2F2-sqrt%286135%29%2F2



So the solutions are:

x=-79%2F2%2Bsqrt%286135%29%2F2 or x=-79%2F2-sqrt%286135%29%2F2