0=-12x^2-20x+8

Solution for 0=-12x^2-20x+8 equation:

0=-12x^2-20x+8

We move all terms to the left:

0-(-12x^2-20x+8)=0

We add all the numbers together, and all the variables

-(-12x^2-20x+8)=0

We get rid of parentheses

12x^2+20x-8=0

a = 12; b = 20; c = -8;
Δ = b2-4ac
Δ = 202-4·12·(-8)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-28}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+28}{2*12}=\frac{8}{24}
=1/3
$