SOLUTION: 2x+3=4x^2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 2x+3=4x^2      Log On


   

Question 146048: 2x+3=4x^2
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3=4x^2
0 = 4x^2 - 2x - 3
.
First, consider factoring -- if that doesn't work, you must 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-2x%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=%28-2%29%5E2-4%2A4%2A-3=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+52+%29%29%2F2%5C4+=+1.151387818866
x%5B2%5D+=+%28-%28-2%29-sqrt%28+52+%29%29%2F2%5C4+=+-0.651387818865997

Quadratic expression 4x%5E2%2B-2x%2B-3 can be factored:
4x%5E2%2B-2x%2B-3+=+4%28x-1.151387818866%29%2A%28x--0.651387818865997%29
Again, the answer is: 1.151387818866, -0.651387818865997. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-2%2Ax%2B-3+%29