(2y-3)(7y-1)=0

Solution for (2y-3)(7y-1)=0 equation:

(2y-3)(7y-1)=0

We multiply parentheses ..

(+14y^2-2y-21y+3)=0

We get rid of parentheses

14y^2-2y-21y+3=0

We add all the numbers together, and all the variables

14y^2-23y+3=0

a = 14; b = -23; c = +3;
Δ = b2-4ac
Δ = -232-4·14·3
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-19}{2*14}=\frac{4}{28}
=1/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+19}{2*14}=\frac{42}{28}
=1+1/2
$