9900=20x+2x^2

Solution for 9900=20x+2x^2 equation:

9900=20x+2x^2

We move all terms to the left:

9900-(20x+2x^2)=0

We get rid of parentheses

-2x^2-20x+9900=0

a = -2; b = -20; c = +9900;
Δ = b2-4ac
Δ = -202-4·(-2)·9900
Δ = 79600
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:

$\sqrt{\Delta}=\sqrt{79600}=\sqrt{400*199}=\sqrt{400}*\sqrt{199}=20\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{199}}{2*-2}=\frac{20-20\sqrt{199}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{199}}{2*-2}=\frac{20+20\sqrt{199}}{-4}
$