4200=50x^2-200x

Solution for 4200=50x^2-200x equation:

4200=50x^2-200x

We move all terms to the left:

4200-(50x^2-200x)=0

We get rid of parentheses

-50x^2+200x+4200=0

a = -50; b = 200; c = +4200;
Δ = b2-4ac
Δ = 2002-4·(-50)·4200
Δ = 880000
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:

$\sqrt{\Delta}=\sqrt{880000}=\sqrt{40000*22}=\sqrt{40000}*\sqrt{22}=200\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200\sqrt{22}}{2*-50}=\frac{-200-200\sqrt{22}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200\sqrt{22}}{2*-50}=\frac{-200+200\sqrt{22}}{-100}
$