-3t(t+8)=0

Solution for -3t(t+8)=0 equation:

-3t(t+8)=0

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