2-x/4+1/2x=3/4x

Solution for 2-x/4+1/2x=3/4x equation:

2-x/4+1/2x=3/4x

We move all terms to the left:

2-x/4+1/2x-(3/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x/4+1/2x-(+3/4x)+2=0

We get rid of parentheses

-x/4+1/2x-3/4x+2=0

We calculate fractions


(-2x^2)/128x^2+64x/128x^2+(-6x)/128x^2+2=0

We multiply all the terms by the denominator


(-2x^2)+64x+(-6x)+2*128x^2=0

Wy multiply elements

(-2x^2)+256x^2+64x+(-6x)=0

We get rid of parentheses

-2x^2+256x^2+64x-6x=0

We add all the numbers together, and all the variables

254x^2+58x=0

a = 254; b = 58; c = 0;
Δ = b2-4ac
Δ = 582-4·254·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-58}{2*254}=\frac{-116}{508}
=-29/127
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+58}{2*254}=\frac{0}{508}
=0
$