(3y-8)(6y-2)=0

Solution for (3y-8)(6y-2)=0 equation:

(3y-8)(6y-2)=0

We multiply parentheses ..

(+18y^2-6y-48y+16)=0

We get rid of parentheses

18y^2-6y-48y+16=0

We add all the numbers together, and all the variables

18y^2-54y+16=0

a = 18; b = -54; c = +16;
Δ = b2-4ac
Δ = -542-4·18·16
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-42}{2*18}=\frac{12}{36}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+42}{2*18}=\frac{96}{36}
=2+2/3
$