9p^2=2

Solution for 9p^2=2 equation:

9p^2=2

We move all terms to the left:

9p^2-(2)=0

a = 9; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·9·(-2)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*9}=\frac{0-6\sqrt{2}}{18}
=-\frac{6\sqrt{2}}{18}
=-\frac{\sqrt{2}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*9}=\frac{0+6\sqrt{2}}{18}
=\frac{6\sqrt{2}}{18}
=\frac{\sqrt{2}}{3}
$