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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-256x^2)/128x^2+64x/128x^2+(-48x)/128x^2-4=0

We multiply all the terms by the denominator


(-256x^2)+64x+(-48x)-4*128x^2=0

Wy multiply elements

(-256x^2)-512x^2+64x+(-48x)=0

We get rid of parentheses

-256x^2-512x^2+64x-48x=0

We add all the numbers together, and all the variables

-768x^2+16x=0

a = -768; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-768)·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*-768}=\frac{-32}{-1536}
=1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-768}=\frac{0}{-1536}
=0
$