4(y+6)y=2

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

4(y+6)y=2

We move all terms to the left:

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

We multiply parentheses

4y^2+24y-2=0

a = 4; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·4·(-2)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{38}}{2*4}=\frac{-24-4\sqrt{38}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{38}}{2*4}=\frac{-24+4\sqrt{38}}{8}
$