-0.5x+1=1/2x-1

Solution for -0.5x+1=1/2x-1 equation:

-0.5x+1=1/2x-1

We move all terms to the left:

-0.5x+1-(1/2x-1)=0


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

-0.5x-1/2x+1+1=0

We multiply all the terms by the denominator


-(0.5x)*2x+1*2x+1*2x-1=0

We add all the numbers together, and all the variables

-(+0.5x)*2x+1*2x+1*2x-1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -1; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-1)·(-1)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{3}}{2*-1}=\frac{-4-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{3}}{2*-1}=\frac{-4+2\sqrt{3}}{-2}
$