8x-12=2x^2-3x

Solution for 8x-12=2x^2-3x equation:

8x-12=2x^2-3x

We move all terms to the left:

8x-12-(2x^2-3x)=0

We get rid of parentheses

-2x^2+8x+3x-12=0

We add all the numbers together, and all the variables

-2x^2+11x-12=0

a = -2; b = 11; c = -12;
Δ = b2-4ac
Δ = 112-4·(-2)·(-12)
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{-(11)-5}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-2}=\frac{-6}{-4}
=1+1/2
$