0=-6x^2+60x-96

Solution for 0=-6x^2+60x-96 equation:

0=-6x^2+60x-96

We move all terms to the left:

0-(-6x^2+60x-96)=0

We add all the numbers together, and all the variables

-(-6x^2+60x-96)=0

We get rid of parentheses

6x^2-60x+96=0

a = 6; b = -60; c = +96;
Δ = b2-4ac
Δ = -602-4·6·96
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-36}{2*6}=\frac{24}{12}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+36}{2*6}=\frac{96}{12}
=8
$