(5y-2)(6y-7)=0

Solution for (5y-2)(6y-7)=0 equation:

(5y-2)(6y-7)=0

We multiply parentheses ..

(+30y^2-35y-12y+14)=0

We get rid of parentheses

30y^2-35y-12y+14=0

We add all the numbers together, and all the variables

30y^2-47y+14=0

a = 30; b = -47; c = +14;
Δ = b2-4ac
Δ = -472-4·30·14
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-23}{2*30}=\frac{24}{60}
=2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+23}{2*30}=\frac{70}{60}
=1+1/6
$