0=-2x^2+20x+50

Solution for 0=-2x^2+20x+50 equation:

0=-2x^2+20x+50

We move all terms to the left:

0-(-2x^2+20x+50)=0

We add all the numbers together, and all the variables

-(-2x^2+20x+50)=0

We get rid of parentheses

2x^2-20x-50=0

a = 2; b = -20; c = -50;
Δ = b2-4ac
Δ = -202-4·2·(-50)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{2}}{2*2}=\frac{20-20\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{2}}{2*2}=\frac{20+20\sqrt{2}}{4}
$