3+3/4x=x/2x

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

3+3/4x=x/2x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

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

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

We get rid of parentheses

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

We calculate fractions


(-4x^2)/8x^2+6x/8x^2+3=0

We multiply all the terms by the denominator


(-4x^2)+6x+3*8x^2=0

Wy multiply elements

(-4x^2)+24x^2+6x=0

We get rid of parentheses

-4x^2+24x^2+6x=0

We add all the numbers together, and all the variables

20x^2+6x=0

a = 20; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·20·0
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*20}=\frac{-12}{40}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*20}=\frac{0}{40}
=0
$