(5)/(8)x-(1)/(3)=(5)/(12)x=(5)/(6)

Solution for (5)/(8)x-(1)/(3)=(5)/(12)x=(5)/(6) equation:

(5)/(8)x-(1)/(3)=(5)/(12)x=(5)/(6)

We move all terms to the left:

(5)/(8)x-(1)/(3)-((5)/(12)x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-(+5/12x)-1/3=0

We get rid of parentheses

5/8x-5/12x-1/3=0

We calculate fractions


(-96x^2)/864x^2+540x/864x^2+(-360x)/864x^2=0

We multiply all the terms by the denominator


(-96x^2)+540x+(-360x)=0

We get rid of parentheses

-96x^2+540x-360x=0

We add all the numbers together, and all the variables

-96x^2+180x=0

a = -96; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-96)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-96}=\frac{-360}{-192}
=1+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-96}=\frac{0}{-192}
=0
$