6/x=-4/3x+6

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

6/x=-4/3x+6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


18x/3x^2+4x/3x^2-6=0

We multiply all the terms by the denominator


18x+4x-6*3x^2=0

We add all the numbers together, and all the variables

22x-6*3x^2=0

Wy multiply elements

-18x^2+22x=0

a = -18; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-18)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-18}=\frac{-44}{-36}
=1+2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-18}=\frac{0}{-36}
=0
$