(3y-6)(y-7)=0

Solution for (3y-6)(y-7)=0 equation:

(3y-6)(y-7)=0

We multiply parentheses ..

(+3y^2-21y-6y+42)=0

We get rid of parentheses

3y^2-21y-6y+42=0

We add all the numbers together, and all the variables

3y^2-27y+42=0

a = 3; b = -27; c = +42;
Δ = b2-4ac
Δ = -272-4·3·42
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-15}{2*3}=\frac{12}{6}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+15}{2*3}=\frac{42}{6}
=7
$