(3y-1)(2y+1)=54

Solution for (3y-1)(2y+1)=54 equation:

(3y-1)(2y+1)=54

We move all terms to the left:

(3y-1)(2y+1)-(54)=0

We multiply parentheses ..

(+6y^2+3y-2y-1)-54=0

We get rid of parentheses

6y^2+3y-2y-1-54=0

We add all the numbers together, and all the variables

6y^2+y-55=0

a = 6; b = 1; c = -55;
Δ = b2-4ac
Δ = 12-4·6·(-55)
Δ = 1321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1321}}{2*6}=\frac{-1-\sqrt{1321}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1321}}{2*6}=\frac{-1+\sqrt{1321}}{12}
$