/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


Domain of the equation: 6(x+1)(x-1)!=0

x∈R


We use the square of the difference formula

x^2-(13x-12)-1=0

We get rid of parentheses

x^2-13x+12-1=0

We add all the numbers together, and all the variables

x^2-13x+11=0

a = 1; b = -13; c = +11;
Δ = b2-4ac
Δ = -132-4·1·11
Δ = 125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5\sqrt{5}}{2*1}=\frac{13-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5\sqrt{5}}{2*1}=\frac{13+5\sqrt{5}}{2}
$