30=-4t^2+24t

Solution for 30=-4t^2+24t equation:

30=-4t^2+24t

We move all terms to the left:

30-(-4t^2+24t)=0

We get rid of parentheses

4t^2-24t+30=0

a = 4; b = -24; c = +30;
Δ = b2-4ac
Δ = -242-4·4·30
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*4}=\frac{24-4\sqrt{6}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{6}}{2*4}=\frac{24+4\sqrt{6}}{8}
$