1/3x+x+2x=80

Solution for 1/3x+x+2x=80 equation:

1/3x+x+2x=80

We move all terms to the left:

1/3x+x+2x-(80)=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-80=0

We multiply all the terms by the denominator


3x*3x-80*3x+1=0

Wy multiply elements

9x^2-240x+1=0

a = 9; b = -240; c = +1;
Δ = b2-4ac
Δ = -2402-4·9·1
Δ = 57564
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:

$\sqrt{\Delta}=\sqrt{57564}=\sqrt{36*1599}=\sqrt{36}*\sqrt{1599}=6\sqrt{1599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-6\sqrt{1599}}{2*9}=\frac{240-6\sqrt{1599}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+6\sqrt{1599}}{2*9}=\frac{240+6\sqrt{1599}}{18}
$