x^2-24x-400=0

Solution for x^2-24x-400=0 equation:

x^2-24x-400=0

a = 1; b = -24; c = -400;
Δ = b2-4ac
Δ = -242-4·1·(-400)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{34}}{2*1}=\frac{24-8\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{34}}{2*1}=\frac{24+8\sqrt{34}}{2}
$