5/3x-2=6+1/4x

Solution for 5/3x-2=6+1/4x equation:

5/3x-2=6+1/4x

We move all terms to the left:

5/3x-2-(6+1/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(1/4x+6)-2=0

We get rid of parentheses

5/3x-1/4x-6-2=0

We calculate fractions


20x/12x^2+(-3x)/12x^2-6-2=0

We add all the numbers together, and all the variables

20x/12x^2+(-3x)/12x^2-8=0

We multiply all the terms by the denominator


20x+(-3x)-8*12x^2=0

Wy multiply elements

-96x^2+20x+(-3x)=0

We get rid of parentheses

-96x^2+20x-3x=0

We add all the numbers together, and all the variables

-96x^2+17x=0

a = -96; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-96)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-96}=\frac{-34}{-192}
=17/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-96}=\frac{0}{-192}
=0
$