6(X-1)(x-1)=13x-12

Solution for 6(X-1)(x-1)=13x-12 equation:

6(X-1)(X-1)=13X-12

We move all terms to the left:

6(X-1)(X-1)-(13X-12)=0

We get rid of parentheses

6(X-1)(X-1)-13X+12=0

We multiply parentheses ..

6(+X^2-1X-1X+1)-13X+12=0

We multiply parentheses

6X^2-6X-6X-13X+6+12=0

We add all the numbers together, and all the variables

6X^2-25X+18=0

a = 6; b = -25; c = +18;
Δ = b2-4ac
Δ = -252-4·6·18
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{193}}{2*6}=\frac{25-\sqrt{193}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{193}}{2*6}=\frac{25+\sqrt{193}}{12}
$