x+x-1/2x=6

Solution for x+x-1/2x=6 equation:

x+x-1/2x=6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/2x-6=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-12x-1=0

a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8}
$