0=-5x^2-50x+100

Solution for 0=-5x^2-50x+100 equation:

0=-5x^2-50x+100

We move all terms to the left:

0-(-5x^2-50x+100)=0

We add all the numbers together, and all the variables

-(-5x^2-50x+100)=0

We get rid of parentheses

5x^2+50x-100=0

a = 5; b = 50; c = -100;
Δ = b2-4ac
Δ = 502-4·5·(-100)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30\sqrt{5}}{2*5}=\frac{-50-30\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30\sqrt{5}}{2*5}=\frac{-50+30\sqrt{5}}{10}
$