0=x^2+24x-400

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

0=x^2+24x-400

We move all terms to the left:

0-(x^2+24x-400)=0

We add all the numbers together, and all the variables

-(x^2+24x-400)=0

We get rid of parentheses

-x^2-24x+400=0

We add all the numbers together, and all the variables

-1x^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}
$