6t^2+6t=30

Solution for 6t^2+6t=30 equation:

6t^2+6t=30

We move all terms to the left:

6t^2+6t-(30)=0

a = 6; b = 6; c = -30;
Δ = b2-4ac
Δ = 62-4·6·(-30)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{21}}{2*6}=\frac{-6-6\sqrt{21}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{21}}{2*6}=\frac{-6+6\sqrt{21}}{12}
$