3/x=-8/3x+4

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

3/x=-8/3x+4

We move all terms to the left:

3/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

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

We calculate fractions


9x/3x^2+8x/3x^2-4=0

We multiply all the terms by the denominator


9x+8x-4*3x^2=0

We add all the numbers together, and all the variables

17x-4*3x^2=0

Wy multiply elements

-12x^2+17x=0

a = -12; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-12)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-12}=\frac{-34}{-24}
=1+5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-12}=\frac{0}{-24}
=0
$