8y(y-6)=16

Solution for 8y(y-6)=16 equation:

8y(y-6)=16

We move all terms to the left:

8y(y-6)-(16)=0

We multiply parentheses

8y^2-48y-16=0

a = 8; b = -48; c = -16;
Δ = b2-4ac
Δ = -482-4·8·(-16)
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16\sqrt{11}}{2*8}=\frac{48-16\sqrt{11}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16\sqrt{11}}{2*8}=\frac{48+16\sqrt{11}}{16}
$