9p^2=15+4p

Solution for 9p^2=15+4p equation:

9p^2=15+4p

We move all terms to the left:

9p^2-(15+4p)=0

We add all the numbers together, and all the variables

9p^2-(4p+15)=0

We get rid of parentheses

9p^2-4p-15=0

a = 9; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·9·(-15)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{139}}{2*9}=\frac{4-2\sqrt{139}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{139}}{2*9}=\frac{4+2\sqrt{139}}{18}
$