(y-6)(y-12)=0

Solution for (y-6)(y-12)=0 equation:

(y-6)(y-12)=0

We multiply parentheses ..

(+y^2-12y-6y+72)=0

We get rid of parentheses

y^2-12y-6y+72=0

We add all the numbers together, and all the variables

y^2-18y+72=0

a = 1; b = -18; c = +72;
Δ = b2-4ac
Δ = -182-4·1·72
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*1}=\frac{12}{2}
=6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*1}=\frac{24}{2}
=12
$