2/4x-1/2=5+3/8x

Solution for 2/4x-1/2=5+3/8x equation:

2/4x-1/2=5+3/8x

We move all terms to the left:

2/4x-1/2-(5+3/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/4x-(3/8x+5)-1/2=0

We get rid of parentheses

2/4x-3/8x-5-1/2=0

We calculate fractions


(-256x^2)/128x^2+64x/128x^2+(-48x)/128x^2-5=0

We multiply all the terms by the denominator


(-256x^2)+64x+(-48x)-5*128x^2=0

Wy multiply elements

(-256x^2)-640x^2+64x+(-48x)=0

We get rid of parentheses

-256x^2-640x^2+64x-48x=0

We add all the numbers together, and all the variables

-896x^2+16x=0

a = -896; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-896)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-896}=\frac{-32}{-1792}
=1/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-896}=\frac{0}{-1792}
=0
$