4/x=5/3x-6

Solution for 4/x=5/3x-6 equation:

4/x=5/3x-6

We move all terms to the left:

4/x-(5/3x-6)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

4/x-5/3x+6=0

We calculate fractions


12x/3x^2+(-5x)/3x^2+6=0

We multiply all the terms by the denominator


12x+(-5x)+6*3x^2=0

Wy multiply elements

18x^2+12x+(-5x)=0

We get rid of parentheses

18x^2+12x-5x=0

We add all the numbers together, and all the variables

18x^2+7x=0

a = 18; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·18·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*18}=\frac{-14}{36}
=-7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*18}=\frac{0}{36}
=0
$