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

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

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

6x^2/8x+4x/8x-5=0

We multiply all the terms by the denominator


6x^2+4x-5*8x=0

Wy multiply elements

6x^2+4x-40x=0

We add all the numbers together, and all the variables

6x^2-36x=0

a = 6; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·6·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*6}=\frac{72}{12}
=6
$