4x+3/4-4x/x-4=x

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

4x+3/4-4x/x-4=x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


3x+(-16x)/4x+3x/4x-4=0

We multiply all the terms by the denominator


3x*4x+(-16x)+3x-4*4x=0

We add all the numbers together, and all the variables

3x+3x*4x+(-16x)-4*4x=0

Wy multiply elements

12x^2+3x+(-16x)-16x=0

We get rid of parentheses

12x^2+3x-16x-16x=0

We add all the numbers together, and all the variables

12x^2-29x=0

a = 12; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·12·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*12}=\frac{58}{24}
=2+5/12
$