3p+63=p2

Solution for 3p+63=p2 equation:

3p+63=p2

We move all terms to the left:

3p+63-(p2)=0

We add all the numbers together, and all the variables

-1p^2+3p+63=0

a = -1; b = 3; c = +63;
Δ = b2-4ac
Δ = 32-4·(-1)·63
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{29}}{2*-1}=\frac{-3-3\sqrt{29}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{29}}{2*-1}=\frac{-3+3\sqrt{29}}{-2}
$