X^2+6x=288

Solution for X^2+6x=288 equation:

X^2+6X=288

We move all terms to the left:

X^2+6X-(288)=0

a = 1; b = 6; c = -288;
Δ = b2-4ac
Δ = 62-4·1·(-288)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{33}}{2*1}=\frac{-6-6\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{33}}{2*1}=\frac{-6+6\sqrt{33}}{2}
$