4(x+1)(x-1)-11X=4(x-2)(x-1)-12

Solution for 4(x+1)(x-1)-11X=4(x-2)(x-1)-12 equation:

4(x+1)(x-1)-11x=4(x-2)(x-1)-12

We move all terms to the left:

4(x+1)(x-1)-11x-(4(x-2)(x-1)-12)=0

We add all the numbers together, and all the variables

-11x+4(x+1)(x-1)-(4(x-2)(x-1)-12)=0

We use the square of the difference formula

x^2-11x-(4(x-2)(x-1)-12)-1=0

We multiply parentheses ..

x^2-(4(+x^2-1x-2x+2)-12)-11x-1=0


We calculate terms in parentheses: -(4(+x^2-1x-2x+2)-12), so:

4(+x^2-1x-2x+2)-12

We multiply parentheses

4x^2-4x-8x+8-12

We add all the numbers together, and all the variables

4x^2-12x-4

Back to the equation:

-(4x^2-12x-4)


We add all the numbers together, and all the variables

x^2-11x-(4x^2-12x-4)-1=0

We get rid of parentheses

x^2-4x^2-11x+12x+4-1=0

We add all the numbers together, and all the variables

-3x^2+x+3=0

a = -3; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-3)·3
Δ = 37
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{-(1)-\sqrt{37}}{2*-3}=\frac{-1-\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*-3}=\frac{-1+\sqrt{37}}{-6}
$