25*X*(200*x+200)-5512,5=0

Solution for 25*X*(200*x+200)-5512,5=0 equation:

25X(200X+200)-5512.5=0

We multiply parentheses

5000X^2+5000X-5512.5=0

a = 5000; b = 5000; c = -5512.5;
Δ = b2-4ac
Δ = 50002-4·5000·(-5512.5)
Δ = 135250000
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:

$\sqrt{\Delta}=\sqrt{135250000}=\sqrt{250000*541}=\sqrt{250000}*\sqrt{541}=500\sqrt{541}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-500\sqrt{541}}{2*5000}=\frac{-5000-500\sqrt{541}}{10000}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+500\sqrt{541}}{2*5000}=\frac{-5000+500\sqrt{541}}{10000}
$