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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


3x*4x+(-8x)+3x+1*4x=0

We add all the numbers together, and all the variables

3x+3x*4x+(-8x)+1*4x=0

Wy multiply elements

12x^2+3x+(-8x)+4x=0

We get rid of parentheses

12x^2+3x-8x+4x=0

We add all the numbers together, and all the variables

12x^2-1x=0

a = 12; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*12}=\frac{2}{24}
=1/12
$