y(4y+8)=32

Solution for y(4y+8)=32 equation:

y(4y+8)=32

We move all terms to the left:

y(4y+8)-(32)=0

We multiply parentheses

4y^2+8y-32=0

a = 4; b = 8; c = -32;
Δ = b2-4ac
Δ = 82-4·4·(-32)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24}{2*4}=\frac{-32}{8}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*4}=\frac{16}{8}
=2
$