5/6x-1/9x=-120

Solution for 5/6x-1/9x=-120 equation:

5/6x-1/9x=-120

We move all terms to the left:

5/6x-1/9x-(-120)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-1/9x+120=0

We calculate fractions


45x/54x^2+(-6x)/54x^2+120=0

We multiply all the terms by the denominator


45x+(-6x)+120*54x^2=0

Wy multiply elements

6480x^2+45x+(-6x)=0

We get rid of parentheses

6480x^2+45x-6x=0

We add all the numbers together, and all the variables

6480x^2+39x=0

a = 6480; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·6480·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*6480}=\frac{-78}{12960}
=-13/2160
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*6480}=\frac{0}{12960}
=0
$