9p^2=6=42

Solution for 9p^2=6=42 equation:

9p^2=6=42

We move all terms to the left:

9p^2-(6)=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:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$p_{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}
$
$p_{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}
$