p^2-9=4p+57

Solution for p^2-9=4p+57 equation:

p^2-9=4p+57

We move all terms to the left:

p^2-9-(4p+57)=0

We get rid of parentheses

p^2-4p-57-9=0

We add all the numbers together, and all the variables

p^2-4p-66=0

a = 1; b = -4; c = -66;
Δ = b2-4ac
Δ = -42-4·1·(-66)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{70}}{2*1}=\frac{4-2\sqrt{70}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{70}}{2*1}=\frac{4+2\sqrt{70}}{2}
$