5x+2x^2-12=4x+4x^2-15

Solution for 5x+2x^2-12=4x+4x^2-15 equation:

5x+2x^2-12=4x+4x^2-15

We move all terms to the left:

5x+2x^2-12-(4x+4x^2-15)=0

We get rid of parentheses

2x^2-4x^2-4x+5x+15-12=0

We add all the numbers together, and all the variables

-2x^2+x+3=0

a = -2; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-2)·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-2}=\frac{4}{-4}
=-1
$