x(x+)=288

Solution for x(x+)=288 equation:

x(x+)=288

We move all terms to the left:

x(x+)-(288)=0

We add all the numbers together, and all the variables

x(+x)-288=0

We multiply parentheses

x^2-288=0

a = 1; b = 0; c = -288;
Δ = b2-4ac
Δ = 02-4·1·(-288)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*1}=\frac{0-24\sqrt{2}}{2}
=-\frac{24\sqrt{2}}{2}
=-12\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*1}=\frac{0+24\sqrt{2}}{2}
=\frac{24\sqrt{2}}{2}
=12\sqrt{2}
$