p2=54-3p

Solution for p2=54-3p equation:

p2=54-3p

We move all terms to the left:

p2-(54-3p)=0

We add all the numbers together, and all the variables

p2-(-3p+54)=0

We add all the numbers together, and all the variables

p^2-(-3p+54)=0

We get rid of parentheses

p^2+3p-54=0

a = 1; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*1}=\frac{-18}{2}
=-9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*1}=\frac{12}{2}
=6
$