SOLUTION: Solve by using Quadratic Formula 12x^2-10x-3=0 5x^2+4x-5=0

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Question 18837: Solve by using Quadratic Formula
12x^2-10x-3=0



5x^2+4x-5=0
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
The solutions to 12x%5E2-10x-3=0+ are
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-10x%2B-3+=+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=%28-10%29%5E2-4%2A12%2A-3=244.

Discriminant d=244 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+244+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+244+%29%29%2F2%5C12+=+1.06752080632555
x%5B2%5D+=+%28-%28-10%29-sqrt%28+244+%29%29%2F2%5C12+=+-0.234187472992221

Quadratic expression 12x%5E2%2B-10x%2B-3 can be factored:
12x%5E2%2B-10x%2B-3+=+%28x-1.06752080632555%29%2A%28x--0.234187472992221%29
Again, the answer is: 1.06752080632555, -0.234187472992221. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-10%2Ax%2B-3+%29


The solutions to 5x%5E2%2B4x-5=0 are
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B4x%2B-5+=+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=%284%29%5E2-4%2A5%2A-5=116.

Discriminant d=116 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+116+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+116+%29%29%2F2%5C5+=+0.677032961426901
x%5B2%5D+=+%28-%284%29-sqrt%28+116+%29%29%2F2%5C5+=+-1.4770329614269

Quadratic expression 5x%5E2%2B4x%2B-5 can be factored:
5x%5E2%2B4x%2B-5+=+%28x-0.677032961426901%29%2A%28x--1.4770329614269%29
Again, the answer is: 0.677032961426901, -1.4770329614269. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B4%2Ax%2B-5+%29