2x+(x1)=1/2x+6

Solution for 2x+(x1)=1/2x+6 equation:

2x+(x1)=1/2x+6

We move all terms to the left:

2x+(x1)-(1/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We add all the numbers together, and all the variables

3x-(1/2x+6)=0

We get rid of parentheses

3x-1/2x-6=0

We multiply all the terms by the denominator


3x*2x-6*2x-1=0

Wy multiply elements

6x^2-12x-1=0

a = 6; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·6·(-1)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{42}}{2*6}=\frac{12-2\sqrt{42}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{42}}{2*6}=\frac{12+2\sqrt{42}}{12}
$