3/x+1-1/6=1/4x+4

Solution for 3/x+1-1/6=1/4x+4 equation:

3/x+1-1/6=1/4x+4

We move all terms to the left:

3/x+1-1/6-(1/4x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

3/x-1/4x-4+1-1/6=0

We calculate fractions


(-16x^2)/144x^2+432x/144x^2+(-36x)/144x^2-4+1=0

We add all the numbers together, and all the variables

(-16x^2)/144x^2+432x/144x^2+(-36x)/144x^2-3=0

We multiply all the terms by the denominator


(-16x^2)+432x+(-36x)-3*144x^2=0

Wy multiply elements

(-16x^2)-432x^2+432x+(-36x)=0

We get rid of parentheses

-16x^2-432x^2+432x-36x=0

We add all the numbers together, and all the variables

-448x^2+396x=0

a = -448; b = 396; c = 0;
Δ = b2-4ac
Δ = 3962-4·(-448)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-396}{2*-448}=\frac{-792}{-896}
=99/112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+396}{2*-448}=\frac{0}{-896}
=0
$