(180x-0.5x^2)-(2000+0.25x^2)=0

Solution for (180x-0.5x^2)-(2000+0.25x^2)=0 equation:

(180x-0.5x^2)-(2000+0.25x^2)=0

We get rid of parentheses

-0.5x^2-0.25x^2+180x-2000=0

We add all the numbers together, and all the variables

-0.75x^2+180x-2000=0

a = -0.75; b = 180; c = -2000;
Δ = b2-4ac
Δ = 1802-4·(-0.75)·(-2000)
Δ = 26400
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:

$\sqrt{\Delta}=\sqrt{26400}=\sqrt{400*66}=\sqrt{400}*\sqrt{66}=20\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-20\sqrt{66}}{2*-0.75}=\frac{-180-20\sqrt{66}}{-1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+20\sqrt{66}}{2*-0.75}=\frac{-180+20\sqrt{66}}{-1.5}
$