SOLUTION: 4x^2=13x+12

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Question 261835: 4x^2=13x+12
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 4x%5E2+=+13x+%2B+12
Rewrite the equation
4x%5E2+-+13x+-+12+=+0
Use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-13x%2B-12+=+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=%28-13%29%5E2-4%2A4%2A-12=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+361+%29%29%2F2%5C4+=+4
x%5B2%5D+=+%28-%28-13%29-sqrt%28+361+%29%29%2F2%5C4+=+-0.75

Quadratic expression 4x%5E2%2B-13x%2B-12 can be factored:
4x%5E2%2B-13x%2B-12+=+4%28x-4%29%2A%28x--0.75%29
Again, the answer is: 4, -0.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-13%2Ax%2B-12+%29