U+6=9x2

Solution for U+6=9x2 equation:

+6=9U^2

We move all terms to the left:

+6-(9U^2)=0

a = -9; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-9)·6
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-9}=\frac{0-6\sqrt{6}}{-18}
=-\frac{6\sqrt{6}}{-18}
=-\frac{\sqrt{6}}{-3}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-9}=\frac{0+6\sqrt{6}}{-18}
=\frac{6\sqrt{6}}{-18}
=\frac{\sqrt{6}}{-3}
$