4y(y-6)+8y=2

Solution for 4y(y-6)+8y=2 equation:

4y(y-6)+8y=2

We move all terms to the left:

4y(y-6)+8y-(2)=0

We add all the numbers together, and all the variables

8y+4y(y-6)-2=0

We multiply parentheses

4y^2+8y-24y-2=0

We add all the numbers together, and all the variables

4y^2-16y-2=0

a = 4; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·4·(-2)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*4}=\frac{16-12\sqrt{2}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*4}=\frac{16+12\sqrt{2}}{8}
$