1/3x+3x=7

Solution for 1/3x+3x=7 equation:

1/3x+3x=7

We move all terms to the left:

1/3x+3x-(7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/3x-7=0

We multiply all the terms by the denominator


3x*3x-7*3x+1=0

Wy multiply elements

9x^2-21x+1=0

a = 9; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·9·1
Δ = 405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9\sqrt{5}}{2*9}=\frac{21-9\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9\sqrt{5}}{2*9}=\frac{21+9\sqrt{5}}{18}
$