108=2t^2+6t

Solution for 108=2t^2+6t equation:

108=2t^2+6t

We move all terms to the left:

108-(2t^2+6t)=0

We get rid of parentheses

-2t^2-6t+108=0

a = -2; b = -6; c = +108;
Δ = b2-4ac
Δ = -62-4·(-2)·108
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{-(-6)-30}{2*-2}=\frac{-24}{-4}
=+6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-2}=\frac{36}{-4}
=-9
$