6=2y(y+2)

Solution for 6=2y(y+2) equation:

6=2y(y+2)

We move all terms to the left:

6-(2y(y+2))=0


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

2y(y+2)

We multiply parentheses

2y^2+4y

Back to the equation:

-(2y^2+4y)


We get rid of parentheses

-2y^2-4y+6=0

a = -2; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-2)·6
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-2}=\frac{-4}{-4}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-2}=\frac{12}{-4}
=-3
$