6x^2-6x=288

Solution for 6x^2-6x=288 equation:

6x^2-6x=288

We move all terms to the left:

6x^2-6x-(288)=0

a = 6; b = -6; c = -288;
Δ = b2-4ac
Δ = -62-4·6·(-288)
Δ = 6948
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:

$\sqrt{\Delta}=\sqrt{6948}=\sqrt{36*193}=\sqrt{36}*\sqrt{193}=6\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{193}}{2*6}=\frac{6-6\sqrt{193}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{193}}{2*6}=\frac{6+6\sqrt{193}}{12}
$