6y(y+8)=2y+32

Solution for 6y(y+8)=2y+32 equation:

6y(y+8)=2y+32

We move all terms to the left:

6y(y+8)-(2y+32)=0

We multiply parentheses

6y^2+48y-(2y+32)=0

We get rid of parentheses

6y^2+48y-2y-32=0

We add all the numbers together, and all the variables

6y^2+46y-32=0

a = 6; b = 46; c = -32;
Δ = b2-4ac
Δ = 462-4·6·(-32)
Δ = 2884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{721}}{2*6}=\frac{-46-2\sqrt{721}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{721}}{2*6}=\frac{-46+2\sqrt{721}}{12}
$