6x^2-6x-72=68

Solution for 6x^2-6x-72=68 equation:

6x^2-6x-72=68

We move all terms to the left:

6x^2-6x-72-(68)=0

We add all the numbers together, and all the variables

6x^2-6x-140=0

a = 6; b = -6; c = -140;
Δ = b2-4ac
Δ = -62-4·6·(-140)
Δ = 3396
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:

$\sqrt{\Delta}=\sqrt{3396}=\sqrt{4*849}=\sqrt{4}*\sqrt{849}=2\sqrt{849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{849}}{2*6}=\frac{6-2\sqrt{849}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{849}}{2*6}=\frac{6+2\sqrt{849}}{12}
$