4000-20x=50+20x^2

Solution for 4000-20x=50+20x^2 equation:

4000-20x=50+20x^2

We move all terms to the left:

4000-20x-(50+20x^2)=0

We get rid of parentheses

-20x^2-20x-50+4000=0

We add all the numbers together, and all the variables

-20x^2-20x+3950=0

a = -20; b = -20; c = +3950;
Δ = b2-4ac
Δ = -202-4·(-20)·3950
Δ = 316400
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:

$\sqrt{\Delta}=\sqrt{316400}=\sqrt{400*791}=\sqrt{400}*\sqrt{791}=20\sqrt{791}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{791}}{2*-20}=\frac{20-20\sqrt{791}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{791}}{2*-20}=\frac{20+20\sqrt{791}}{-40}
$