x(x-50)=10000

Solution for x(x-50)=10000 equation:

x(x-50)=10000

We move all terms to the left:

x(x-50)-(10000)=0

We multiply parentheses

x^2-50x-10000=0

a = 1; b = -50; c = -10000;
Δ = b2-4ac
Δ = -502-4·1·(-10000)
Δ = 42500
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:

$\sqrt{\Delta}=\sqrt{42500}=\sqrt{2500*17}=\sqrt{2500}*\sqrt{17}=50\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{17}}{2*1}=\frac{50-50\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{17}}{2*1}=\frac{50+50\sqrt{17}}{2}
$