p^2=4p+45

Solution for p^2=4p+45 equation:

p^2=4p+45

We move all terms to the left:

p^2-(4p+45)=0

We get rid of parentheses

p^2-4p-45=0

a = 1; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·1·(-45)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*1}=\frac{-10}{2}
=-5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*1}=\frac{18}{2}
=9
$