p(6p+5)=18p+15

Solution for p(6p+5)=18p+15 equation:

p(6p+5)=18p+15

We move all terms to the left:

p(6p+5)-(18p+15)=0

We multiply parentheses

6p^2+5p-(18p+15)=0

We get rid of parentheses

6p^2+5p-18p-15=0

We add all the numbers together, and all the variables

6p^2-13p-15=0

a = 6; b = -13; c = -15;
Δ = b2-4ac
Δ = -132-4·6·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*6}=\frac{-10}{12}
=-5/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*6}=\frac{36}{12}
=3
$