x/3x+2x=20

Solution for x/3x+2x=20 equation:

x/3x+2x=20

We move all terms to the left:

x/3x+2x-(20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+x/3x-20=0

We multiply all the terms by the denominator


2x*3x+x-20*3x=0

We add all the numbers together, and all the variables

x+2x*3x-20*3x=0

Wy multiply elements

6x^2+x-60x=0

We add all the numbers together, and all the variables

6x^2-59x=0

a = 6; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·6·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*6}=\frac{118}{12}
=9+5/6
$