0=180x-8x^2-500

Solution for 0=180x-8x^2-500 equation:

0=180x-8x^2-500

We move all terms to the left:

0-(180x-8x^2-500)=0

We add all the numbers together, and all the variables

-(180x-8x^2-500)=0

We get rid of parentheses

8x^2-180x+500=0

a = 8; b = -180; c = +500;
Δ = b2-4ac
Δ = -1802-4·8·500
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-20\sqrt{41}}{2*8}=\frac{180-20\sqrt{41}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+20\sqrt{41}}{2*8}=\frac{180+20\sqrt{41}}{16}
$