1/x=-6/3x-4

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

1/x=-6/3x-4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


3x+6x+4*3x^2=0

We add all the numbers together, and all the variables

9x+4*3x^2=0

Wy multiply elements

12x^2+9x=0

a = 12; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·12·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*12}=\frac{-18}{24}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*12}=\frac{0}{24}
=0
$