5/9x-1/3x=86

Solution for 5/9x-1/3x=86 equation:

5/9x-1/3x=86

We move all terms to the left:

5/9x-1/3x-(86)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x/27x^2+(-9x)/27x^2-86=0

We multiply all the terms by the denominator


15x+(-9x)-86*27x^2=0

Wy multiply elements

-2322x^2+15x+(-9x)=0

We get rid of parentheses

-2322x^2+15x-9x=0

We add all the numbers together, and all the variables

-2322x^2+6x=0

a = -2322; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-2322)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-2322}=\frac{-12}{-4644}
=1/387
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-2322}=\frac{0}{-4644}
=0
$