0=x^2-400-24000

Solution for 0=x^2-400-24000 equation:

0=x^2-400-24000

We move all terms to the left:

0-(x^2-400-24000)=0

We add all the numbers together, and all the variables

-(x^2-400-24000)=0

We get rid of parentheses

-x^2+400+24000=0

We add all the numbers together, and all the variables

-1x^2+24400=0

a = -1; b = 0; c = +24400;
Δ = b2-4ac
Δ = 02-4·(-1)·24400
Δ = 97600
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:

$\sqrt{\Delta}=\sqrt{97600}=\sqrt{1600*61}=\sqrt{1600}*\sqrt{61}=40\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{61}}{2*-1}=\frac{0-40\sqrt{61}}{-2}
=-\frac{40\sqrt{61}}{-2}
=-\frac{20\sqrt{61}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{61}}{2*-1}=\frac{0+40\sqrt{61}}{-2}
=\frac{40\sqrt{61}}{-2}
=\frac{20\sqrt{61}}{-1}
$