2+4/x=7/12x

Solution for 2+4/x=7/12x equation:

2+4/x=7/12x

We move all terms to the left:

2+4/x-(7/12x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(+7/12x)+2=0

We get rid of parentheses

4/x-7/12x+2=0

We calculate fractions


48x/12x^2+(-7x)/12x^2+2=0

We multiply all the terms by the denominator


48x+(-7x)+2*12x^2=0

Wy multiply elements

24x^2+48x+(-7x)=0

We get rid of parentheses

24x^2+48x-7x=0

We add all the numbers together, and all the variables

24x^2+41x=0

a = 24; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·24·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*24}=\frac{-82}{48}
=-1+17/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*24}=\frac{0}{48}
=0
$