32u2=9

Solution for 32u2=9 equation:

32u^2=9

We move all terms to the left:

32u^2-(9)=0

a = 32; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·32·(-9)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*32}=\frac{0-24\sqrt{2}}{64}
=-\frac{24\sqrt{2}}{64}
=-\frac{3\sqrt{2}}{8}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*32}=\frac{0+24\sqrt{2}}{64}
=\frac{24\sqrt{2}}{64}
=\frac{3\sqrt{2}}{8}
$