11/12x+x-(x-2)=x

Solution for 11/12x+x-(x-2)=x equation:

11/12x+x-(x-2)=x

We move all terms to the left:

11/12x+x-(x-2)-(x)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

11/12x-(x-2)=0

We get rid of parentheses

11/12x-x+2=0

We multiply all the terms by the denominator


-x*12x+2*12x+11=0

Wy multiply elements

-12x^2+24x+11=0

a = -12; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·(-12)·11
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{69}}{2*-12}=\frac{-24-4\sqrt{69}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{69}}{2*-12}=\frac{-24+4\sqrt{69}}{-24}
$