5/6x-1/8x=9

Solution for 5/6x-1/8x=9 equation:

5/6x-1/8x=9

We move all terms to the left:

5/6x-1/8x-(9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


40x/48x^2+(-6x)/48x^2-9=0

We multiply all the terms by the denominator


40x+(-6x)-9*48x^2=0

Wy multiply elements

-432x^2+40x+(-6x)=0

We get rid of parentheses

-432x^2+40x-6x=0

We add all the numbers together, and all the variables

-432x^2+34x=0

a = -432; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-432)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-432}=\frac{-68}{-864}
=17/216
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-432}=\frac{0}{-864}
=0
$