6=6t^2-24t-24

Solution for 6=6t^2-24t-24 equation:

6=6t^2-24t-24

We move all terms to the left:

6-(6t^2-24t-24)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6t^2+24t+30=0

a = -6; b = 24; c = +30;
Δ = b2-4ac
Δ = 242-4·(-6)·30
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-36}{2*-6}=\frac{-60}{-12}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*-6}=\frac{12}{-12}
=-1
$