5/6x-1/8x=17/84

Solution for 5/6x-1/8x=17/84 equation:

5/6x-1/8x=17/84

We move all terms to the left:

5/6x-1/8x-(17/84)=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 add all the numbers together, and all the variables

5/6x-1/8x-(+17/84)=0

We get rid of parentheses

5/6x-1/8x-17/84=0

We calculate fractions


(-6528x^2)/32256x^2+26880x/32256x^2+(-4032x)/32256x^2=0

We multiply all the terms by the denominator


(-6528x^2)+26880x+(-4032x)=0

We get rid of parentheses

-6528x^2+26880x-4032x=0

We add all the numbers together, and all the variables

-6528x^2+22848x=0

a = -6528; b = 22848; c = 0;
Δ = b2-4ac
Δ = 228482-4·(-6528)·0
Δ = 522031104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{522031104}=22848$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22848)-22848}{2*-6528}=\frac{-45696}{-13056}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22848)+22848}{2*-6528}=\frac{0}{-13056}
=0
$