108=121.5-1.5u^2

Solution for 108=121.5-1.5u^2 equation:

108=121.5-1.5u^2

We move all terms to the left:

108-(121.5-1.5u^2)=0

We get rid of parentheses

1.5u^2-121.5+108=0

We add all the numbers together, and all the variables

1.5u^2-13.5=0

a = 1.5; b = 0; c = -13.5;
Δ = b2-4ac
Δ = 02-4·1.5·(-13.5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-9}{2*1.5}=\frac{-9}{3}
=-3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+9}{2*1.5}=\frac{9}{3}
=3
$