(5y-2)(12y-7)=0

Solution for (5y-2)(12y-7)=0 equation:

(5y-2)(12y-7)=0

We multiply parentheses ..

(+60y^2-35y-24y+14)=0

We get rid of parentheses

60y^2-35y-24y+14=0

We add all the numbers together, and all the variables

60y^2-59y+14=0

a = 60; b = -59; c = +14;
Δ = b2-4ac
Δ = -592-4·60·14
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-11}{2*60}=\frac{48}{120}
=2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+11}{2*60}=\frac{70}{120}
=7/12
$