x^2-24x-2200=0

Solution for x^2-24x-2200=0 equation:

x^2-24x-2200=0

a = 1; b = -24; c = -2200;
Δ = b2-4ac
Δ = -242-4·1·(-2200)
Δ = 9376
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:

$\sqrt{\Delta}=\sqrt{9376}=\sqrt{16*586}=\sqrt{16}*\sqrt{586}=4\sqrt{586}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{586}}{2*1}=\frac{24-4\sqrt{586}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{586}}{2*1}=\frac{24+4\sqrt{586}}{2}
$