SOLUTION: 3x^2 = 5x+4

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Question 953472: 3x^2 = 5x+4
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+=+5x%2B4
3x%5E2-5x-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-4+=+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=%28-5%29%5E2-4%2A3%2A-4=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+73+%29%29%2F2%5C3+=+2.25733395755292
x%5B2%5D+=+%28-%28-5%29-sqrt%28+73+%29%29%2F2%5C3+=+-0.590667290886255

Quadratic expression 3x%5E2%2B-5x%2B-4 can be factored:
3x%5E2%2B-5x%2B-4+=+3%28x-2.25733395755292%29%2A%28x--0.590667290886255%29
Again, the answer is: 2.25733395755292, -0.590667290886255. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B-4+%29