1/3x+3x=40

Solution for 1/3x+3x=40 equation:

1/3x+3x=40

We move all terms to the left:

1/3x+3x-(40)=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-40=0

We multiply all the terms by the denominator


3x*3x-40*3x+1=0

Wy multiply elements

9x^2-120x+1=0

a = 9; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·9·1
Δ = 14364
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:

$\sqrt{\Delta}=\sqrt{14364}=\sqrt{36*399}=\sqrt{36}*\sqrt{399}=6\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-6\sqrt{399}}{2*9}=\frac{120-6\sqrt{399}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+6\sqrt{399}}{2*9}=\frac{120+6\sqrt{399}}{18}
$