0=500-180x+12x^2

Solution for 0=500-180x+12x^2 equation:

0=500-180x+12x^2

We move all terms to the left:

0-(500-180x+12x^2)=0

We add all the numbers together, and all the variables

-(500-180x+12x^2)=0

We get rid of parentheses

-12x^2+180x-500=0

a = -12; b = 180; c = -500;
Δ = b2-4ac
Δ = 1802-4·(-12)·(-500)
Δ = 8400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-20\sqrt{21}}{2*-12}=\frac{-180-20\sqrt{21}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+20\sqrt{21}}{2*-12}=\frac{-180+20\sqrt{21}}{-24}
$