p2+1=3p+9

Solution for p2+1=3p+9 equation:

p2+1=3p+9

We move all terms to the left:

p2+1-(3p+9)=0

We add all the numbers together, and all the variables

p^2-(3p+9)+1=0

We get rid of parentheses

p^2-3p-9+1=0

We add all the numbers together, and all the variables

p^2-3p-8=0

a = 1; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·1·(-8)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{41}}{2*1}=\frac{3-\sqrt{41}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*1}=\frac{3+\sqrt{41}}{2}
$