2x-6=x1/2x

Solution for 2x-6=x1/2x equation:

2x-6=x1/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-x1/2x-6=0

We multiply all the terms by the denominator


2x*2x-x1-6*2x=0

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-1x-12x=0

We add all the numbers together, and all the variables

4x^2-13x=0

a = 4; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·4·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*4}=\frac{26}{8}
=3+1/4
$