p2+15p=-27

Solution for p2+15p=-27 equation:

p2+15p=-27

We move all terms to the left:

p2+15p-(-27)=0

We add all the numbers together, and all the variables

p^2+15p+27=0

a = 1; b = 15; c = +27;
Δ = b2-4ac
Δ = 152-4·1·27
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{13}}{2*1}=\frac{-15-3\sqrt{13}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{13}}{2*1}=\frac{-15+3\sqrt{13}}{2}
$