6t^2-18t=6

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

6t^2-18t=6

We move all terms to the left:

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

a = 6; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·6·(-6)
Δ = 468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{13}}{2*6}=\frac{18-6\sqrt{13}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{13}}{2*6}=\frac{18+6\sqrt{13}}{12}
$