6x^2-6x=59

Solution for 6x^2-6x=59 equation:

6x^2-6x=59

We move all terms to the left:

6x^2-6x-(59)=0

a = 6; b = -6; c = -59;
Δ = b2-4ac
Δ = -62-4·6·(-59)
Δ = 1452
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:

$\sqrt{\Delta}=\sqrt{1452}=\sqrt{484*3}=\sqrt{484}*\sqrt{3}=22\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-22\sqrt{3}}{2*6}=\frac{6-22\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+22\sqrt{3}}{2*6}=\frac{6+22\sqrt{3}}{12}
$