11/12x+8=x

Solution for 11/12x+8=x equation:

11/12x+8=x

We move all terms to the left:

11/12x+8-(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

-1x+11/12x+8=0

We multiply all the terms by the denominator


-1x*12x+8*12x+11=0

Wy multiply elements

-12x^2+96x+11=0

a = -12; b = 96; c = +11;
Δ = b2-4ac
Δ = 962-4·(-12)·11
Δ = 9744
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:

$\sqrt{\Delta}=\sqrt{9744}=\sqrt{16*609}=\sqrt{16}*\sqrt{609}=4\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{609}}{2*-12}=\frac{-96-4\sqrt{609}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{609}}{2*-12}=\frac{-96+4\sqrt{609}}{-24}
$