0=120-92x+12x^2

Solution for 0=120-92x+12x^2 equation:

0=120-92x+12x^2

We move all terms to the left:

0-(120-92x+12x^2)=0

We add all the numbers together, and all the variables

-(120-92x+12x^2)=0

We get rid of parentheses

-12x^2+92x-120=0

a = -12; b = 92; c = -120;
Δ = b2-4ac
Δ = 922-4·(-12)·(-120)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-52}{2*-12}=\frac{-144}{-24}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+52}{2*-12}=\frac{-40}{-24}
=1+2/3
$