P=(24y+y^2)

Solution for P=(24y+y^2) equation:

=(24P+P^2)

We move all terms to the left:

-((24P+P^2))=0


We calculate terms in parentheses: -((24P+P^2)), so:

(24P+P^2)

We get rid of parentheses

P^2+24P

Back to the equation:

-(P^2+24P)


We get rid of parentheses

-P^2-24P=0

We add all the numbers together, and all the variables

-1P^2-24P=0

a = -1; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-1)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-1}=\frac{0}{-2}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-1}=\frac{48}{-2}
=-24
$