5/6x-1/9x=102

Solution for 5/6x-1/9x=102 equation:

5/6x-1/9x=102

We move all terms to the left:

5/6x-1/9x-(102)=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 calculate fractions


45x/54x^2+(-6x)/54x^2-102=0

We multiply all the terms by the denominator


45x+(-6x)-102*54x^2=0

Wy multiply elements

-5508x^2+45x+(-6x)=0

We get rid of parentheses

-5508x^2+45x-6x=0

We add all the numbers together, and all the variables

-5508x^2+39x=0

a = -5508; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-5508)·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*-5508}=\frac{-78}{-11016}
=13/1836
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-5508}=\frac{0}{-11016}
=0
$