18x^2-6x=6

Solution for 18x^2-6x=6 equation:

18x^2-6x=6

We move all terms to the left:

18x^2-6x-(6)=0

a = 18; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·18·(-6)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{13}}{2*18}=\frac{6-6\sqrt{13}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{13}}{2*18}=\frac{6+6\sqrt{13}}{36}
$