3+7/8x=1/2x

Solution for 3+7/8x=1/2x equation:

3+7/8x=1/2x

We move all terms to the left:

3+7/8x-(1/2x)=0


Domain of the equation: 8x!=0

x!=0/8

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

7/8x-(+1/2x)+3=0

We get rid of parentheses

7/8x-1/2x+3=0

We calculate fractions


14x/16x^2+(-8x)/16x^2+3=0

We multiply all the terms by the denominator


14x+(-8x)+3*16x^2=0

Wy multiply elements

48x^2+14x+(-8x)=0

We get rid of parentheses

48x^2+14x-8x=0

We add all the numbers together, and all the variables

48x^2+6x=0

a = 48; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·48·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*48}=\frac{-12}{96}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*48}=\frac{0}{96}
=0
$