(5y-6)(2y-5)=0

Solution for (5y-6)(2y-5)=0 equation:

(5y-6)(2y-5)=0

We multiply parentheses ..

(+10y^2-25y-12y+30)=0

We get rid of parentheses

10y^2-25y-12y+30=0

We add all the numbers together, and all the variables

10y^2-37y+30=0

a = 10; b = -37; c = +30;
Δ = b2-4ac
Δ = -372-4·10·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-13}{2*10}=\frac{24}{20}
=1+1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+13}{2*10}=\frac{50}{20}
=2+1/2
$