2000=180x-2x^2

Solution for 2000=180x-2x^2 equation:

2000=180x-2x^2

We move all terms to the left:

2000-(180x-2x^2)=0

We get rid of parentheses

2x^2-180x+2000=0

a = 2; b = -180; c = +2000;
Δ = b2-4ac
Δ = -1802-4·2·2000
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*2}=\frac{180-20\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+20\sqrt{41}}{2*2}=\frac{180+20\sqrt{41}}{4}
$