3-x/x=x+1/2x

Solution for 3-x/x=x+1/2x equation:

3-x/x=x+1/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x/x-x-1/2x+3=0

Fractions to decimals

-1/2x-x+3+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+8x-1=0

a = -2; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-2)·(-1)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*-2}=\frac{-8-2\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*-2}=\frac{-8+2\sqrt{14}}{-4}
$