x-2=11/12x

Solution for x-2=11/12x equation:

x-2=11/12x

We move all terms to the left:

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


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-11/12x-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}
$