20x=-16x^2+200

Solution for 20x=-16x^2+200 equation:

20x=-16x^2+200

We move all terms to the left:

20x-(-16x^2+200)=0

We get rid of parentheses

16x^2+20x-200=0

a = 16; b = 20; c = -200;
Δ = b2-4ac
Δ = 202-4·16·(-200)
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{33}}{2*16}=\frac{-20-20\sqrt{33}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{33}}{2*16}=\frac{-20+20\sqrt{33}}{32}
$