(2y-2)(2y-9)=0

Solution for (2y-2)(2y-9)=0 equation:

(2y-2)(2y-9)=0

We multiply parentheses ..

(+4y^2-18y-4y+18)=0

We get rid of parentheses

4y^2-18y-4y+18=0

We add all the numbers together, and all the variables

4y^2-22y+18=0

a = 4; b = -22; c = +18;
Δ = b2-4ac
Δ = -222-4·4·18
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14}{2*4}=\frac{8}{8}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14}{2*4}=\frac{36}{8}
=4+1/2
$