6t^2-30t-72=12

Solution for 6t^2-30t-72=12 equation:

6t^2-30t-72=12

We move all terms to the left:

6t^2-30t-72-(12)=0

We add all the numbers together, and all the variables

6t^2-30t-84=0

a = 6; b = -30; c = -84;
Δ = b2-4ac
Δ = -302-4·6·(-84)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-54}{2*6}=\frac{-24}{12}
=-2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+54}{2*6}=\frac{84}{12}
=7
$