x2-24x=300

Solution for x2-24x=300 equation:

x2-24x=300

We move all terms to the left:

x2-24x-(300)=0

We add all the numbers together, and all the variables

x^2-24x-300=0

a = 1; b = -24; c = -300;
Δ = b2-4ac
Δ = -242-4·1·(-300)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{111}}{2*1}=\frac{24-4\sqrt{111}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{111}}{2*1}=\frac{24+4\sqrt{111}}{2}
$