6t(t+5)=0

Solution for 6t(t+5)=0 equation:

6t(t+5)=0

We multiply parentheses

6t^2+30t=0

a = 6; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·6·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*6}=\frac{-60}{12}
=-5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*6}=\frac{0}{12}
=0
$