6t^2+2t-30=0

Solution for 6t^2+2t-30=0 equation:

6t^2+2t-30=0

a = 6; b = 2; c = -30;
Δ = b2-4ac
Δ = 22-4·6·(-30)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{181}}{2*6}=\frac{-2-2\sqrt{181}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{181}}{2*6}=\frac{-2+2\sqrt{181}}{12}
$