p(p+15)=(3p-15)

Solution for p(p+15)=(3p-15) equation:

p(p+15)=(3p-15)

We move all terms to the left:

p(p+15)-((3p-15))=0

We multiply parentheses

p^2+15p-((3p-15))=0


We calculate terms in parentheses: -((3p-15)), so:

(3p-15)

We get rid of parentheses

3p-15

Back to the equation:

-(3p-15)


We get rid of parentheses

p^2+15p-3p+15=0

We add all the numbers together, and all the variables

p^2+12p+15=0

a = 1; b = 12; c = +15;
Δ = b2-4ac
Δ = 122-4·1·15
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{21}}{2*1}=\frac{-12-2\sqrt{21}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{21}}{2*1}=\frac{-12+2\sqrt{21}}{2}
$