0=-x^2+75x-1200

Solution for 0=-x^2+75x-1200 equation:

0=-x^2+75x-1200

We move all terms to the left:

0-(-x^2+75x-1200)=0

We add all the numbers together, and all the variables

-(-x^2+75x-1200)=0

We get rid of parentheses

x^2-75x+1200=0

a = 1; b = -75; c = +1200;
Δ = b2-4ac
Δ = -752-4·1·1200
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{33}}{2*1}=\frac{75-5\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{33}}{2*1}=\frac{75+5\sqrt{33}}{2}
$