-1/x=-8/3x-4

Solution for -1/x=-8/3x-4 equation:

-1/x=-8/3x-4

We move all terms to the left:

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+5x=0

a = 12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*12}=\frac{-10}{24}
=-5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*12}=\frac{0}{24}
=0
$