SOLUTION: 7x(3x+4)=8(2x+5)+13

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Question 114667: 7x(3x+4)=8(2x+5)+13
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
7x(3x+4)=8(2x+5)+13
21x^2+28x=16x+40+13
21x^2+12x-53=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 21x%5E2%2B12x%2B-53+=+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=%2812%29%5E2-4%2A21%2A-53=4596.

Discriminant d=4596 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+4596+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+4596+%29%29%2F2%5C21+=+1.32842392920746
x%5B2%5D+=+%28-%2812%29-sqrt%28+4596+%29%29%2F2%5C21+=+-1.89985250063603

Quadratic expression 21x%5E2%2B12x%2B-53 can be factored:
21x%5E2%2B12x%2B-53+=+%28x-1.32842392920746%29%2A%28x--1.89985250063603%29
Again, the answer is: 1.32842392920746, -1.89985250063603. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+21%2Ax%5E2%2B12%2Ax%2B-53+%29