x/3x+6+4x=13

Solution for x/3x+6+4x=13 equation:

x/3x+6+4x=13

We move all terms to the left:

x/3x+6+4x-(13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x+x/3x-7=0

We multiply all the terms by the denominator


4x*3x+x-7*3x=0

We add all the numbers together, and all the variables

x+4x*3x-7*3x=0

Wy multiply elements

12x^2+x-21x=0

We add all the numbers together, and all the variables

12x^2-20x=0

a = 12; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·12·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*12}=\frac{40}{24}
=1+2/3
$