-6t^2+24t+10=30

Solution for -6t^2+24t+10=30 equation:

-6t^2+24t+10=30

We move all terms to the left:

-6t^2+24t+10-(30)=0

We add all the numbers together, and all the variables

-6t^2+24t-20=0

a = -6; b = 24; c = -20;
Δ = b2-4ac
Δ = 242-4·(-6)·(-20)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{6}}{2*-6}=\frac{-24-4\sqrt{6}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{6}}{2*-6}=\frac{-24+4\sqrt{6}}{-12}
$