3/4x=2/1x-2

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

3/4x=2/1x-2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 1x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+3x+(-8x)=0

We get rid of parentheses

8x^2+3x-8x=0

We add all the numbers together, and all the variables

8x^2-5x=0

a = 8; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·8·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*8}=\frac{10}{16}
=5/8
$