(3y-1)(2y+1)=5y

Solution for (3y-1)(2y+1)=5y equation:

(3y-1)(2y+1)=5y

We move all terms to the left:

(3y-1)(2y+1)-(5y)=0

We add all the numbers together, and all the variables

-5y+(3y-1)(2y+1)=0

We multiply parentheses ..

(+6y^2+3y-2y-1)-5y=0

We get rid of parentheses

6y^2+3y-2y-5y-1=0

We add all the numbers together, and all the variables

6y^2-4y-1=0

a = 6; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·6·(-1)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*6}=\frac{4-2\sqrt{10}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*6}=\frac{4+2\sqrt{10}}{12}
$