6x^2-6x=52

Solution for 6x^2-6x=52 equation:

6x^2-6x=52

We move all terms to the left:

6x^2-6x-(52)=0

a = 6; b = -6; c = -52;
Δ = b2-4ac
Δ = -62-4·6·(-52)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{321}}{2*6}=\frac{6-2\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{321}}{2*6}=\frac{6+2\sqrt{321}}{12}
$