12=2x2-3x+8

Solution for 12=2x2-3x+8 equation:

12=2x^2-3x+8

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+3x+4=0

a = -2; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-2)·4
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*-2}=\frac{-3-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*-2}=\frac{-3+\sqrt{41}}{-4}
$