9p^2+2=41

Solution for 9p^2+2=41 equation:

9p^2+2=41

We move all terms to the left:

9p^2+2-(41)=0

We add all the numbers together, and all the variables

9p^2-39=0

a = 9; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·9·(-39)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{39}}{2*9}=\frac{0-6\sqrt{39}}{18}
=-\frac{6\sqrt{39}}{18}
=-\frac{\sqrt{39}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{39}}{2*9}=\frac{0+6\sqrt{39}}{18}
=\frac{6\sqrt{39}}{18}
=\frac{\sqrt{39}}{3}
$