9p^2-29=-5

Solution for 9p^2-29=-5 equation:

9p^2-29=-5

We move all terms to the left:

9p^2-29-(-5)=0

We add all the numbers together, and all the variables

9p^2-24=0

a = 9; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·9·(-24)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*9}=\frac{0-12\sqrt{6}}{18}
=-\frac{12\sqrt{6}}{18}
=-\frac{2\sqrt{6}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*9}=\frac{0+12\sqrt{6}}{18}
=\frac{12\sqrt{6}}{18}
=\frac{2\sqrt{6}}{3}
$