x^2-50x=828

Solution for x^2-50x=828 equation:

x^2-50x=828

We move all terms to the left:

x^2-50x-(828)=0

a = 1; b = -50; c = -828;
Δ = b2-4ac
Δ = -502-4·1·(-828)
Δ = 5812
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:

$\sqrt{\Delta}=\sqrt{5812}=\sqrt{4*1453}=\sqrt{4}*\sqrt{1453}=2\sqrt{1453}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1453}}{2*1}=\frac{50-2\sqrt{1453}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1453}}{2*1}=\frac{50+2\sqrt{1453}}{2}
$