24=y(y+2)

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

24=y(y+2)

We move all terms to the left:

24-(y(y+2))=0


We calculate terms in parentheses: -(y(y+2)), so:

y(y+2)

We multiply parentheses

y^2+2y

Back to the equation:

-(y^2+2y)


We get rid of parentheses

-y^2-2y+24=0

We add all the numbers together, and all the variables

-1y^2-2y+24=0

a = -1; b = -2; c = +24;
Δ = b2-4ac
Δ = -22-4·(-1)·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-1}=\frac{-8}{-2}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-1}=\frac{12}{-2}
=-6
$