3t^2=-24t

Solution for 3t^2=-24t equation:

3t^2=-24t

We move all terms to the left:

3t^2-(-24t)=0

We get rid of parentheses

3t^2+24t=0

a = 3; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·3·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*3}=\frac{-48}{6}
=-8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*3}=\frac{0}{6}
=0
$