(2p+15)=p(p+15)

Solution for (2p+15)=p(p+15) equation:

(2p+15)=p(p+15)

We move all terms to the left:

(2p+15)-(p(p+15))=0

We get rid of parentheses

2p-(p(p+15))+15=0


We calculate terms in parentheses: -(p(p+15)), so:

p(p+15)

We multiply parentheses

p^2+15p

Back to the equation:

-(p^2+15p)


We get rid of parentheses

-p^2+2p-15p+15=0

We add all the numbers together, and all the variables

-1p^2-13p+15=0

a = -1; b = -13; c = +15;
Δ = b2-4ac
Δ = -132-4·(-1)·15
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{229}}{2*-1}=\frac{13-\sqrt{229}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{229}}{2*-1}=\frac{13+\sqrt{229}}{-2}
$