x^2-220x=11424

Solution for x^2-220x=11424 equation:

x^2-220x=11424

We move all terms to the left:

x^2-220x-(11424)=0

a = 1; b = -220; c = -11424;
Δ = b2-4ac
Δ = -2202-4·1·(-11424)
Δ = 94096
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:

$\sqrt{\Delta}=\sqrt{94096}=\sqrt{16*5881}=\sqrt{16}*\sqrt{5881}=4\sqrt{5881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-4\sqrt{5881}}{2*1}=\frac{220-4\sqrt{5881}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+4\sqrt{5881}}{2*1}=\frac{220+4\sqrt{5881}}{2}
$