(9y-2)(2y-5)=0

Solution for (9y-2)(2y-5)=0 equation:

(9y-2)(2y-5)=0

We multiply parentheses ..

(+18y^2-45y-4y+10)=0

We get rid of parentheses

18y^2-45y-4y+10=0

We add all the numbers together, and all the variables

18y^2-49y+10=0

a = 18; b = -49; c = +10;
Δ = b2-4ac
Δ = -492-4·18·10
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-41}{2*18}=\frac{8}{36}
=2/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+41}{2*18}=\frac{90}{36}
=2+1/2
$