9(u-2)1.5u=8.25

Solution for 9(u-2)1.5u=8.25 equation:

9(u-2)1.5u=8.25

We move all terms to the left:

9(u-2)1.5u-(8.25)=0

We add all the numbers together, and all the variables

9(u-2)1.5u-8.25=0

We multiply parentheses

9u^2-18u-8.25=0

a = 9; b = -18; c = -8.25;
Δ = b2-4ac
Δ = -182-4·9·(-8.25)
Δ = 621
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-3\sqrt{69}}{2*9}=\frac{18-3\sqrt{69}}{18}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+3\sqrt{69}}{2*9}=\frac{18+3\sqrt{69}}{18}
$