100=-5x^2+100x-250

Solution for 100=-5x^2+100x-250 equation:

100=-5x^2+100x-250

We move all terms to the left:

100-(-5x^2+100x-250)=0

We get rid of parentheses

5x^2-100x+250+100=0

We add all the numbers together, and all the variables

5x^2-100x+350=0

a = 5; b = -100; c = +350;
Δ = b2-4ac
Δ = -1002-4·5·350
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{30}}{2*5}=\frac{100-10\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{30}}{2*5}=\frac{100+10\sqrt{30}}{10}
$