(3f-1)(2f-1)=1

Solution for (3f-1)(2f-1)=1 equation:

(3f-1)(2f-1)=1

We move all terms to the left:

(3f-1)(2f-1)-(1)=0

We multiply parentheses ..

(+6f^2-3f-2f+1)-1=0

We get rid of parentheses

6f^2-3f-2f+1-1=0

We add all the numbers together, and all the variables

6f^2-5f=0

a = 6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·6·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*6}=\frac{0}{12}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*6}=\frac{10}{12}
=5/6
$