1/3x+2x+x=110

Solution for 1/3x+2x+x=110 equation:

1/3x+2x+x=110

We move all terms to the left:

1/3x+2x+x-(110)=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-110=0

We multiply all the terms by the denominator


3x*3x-110*3x+1=0

Wy multiply elements

9x^2-330x+1=0

a = 9; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·9·1
Δ = 108864
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:

$\sqrt{\Delta}=\sqrt{108864}=\sqrt{5184*21}=\sqrt{5184}*\sqrt{21}=72\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-72\sqrt{21}}{2*9}=\frac{330-72\sqrt{21}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+72\sqrt{21}}{2*9}=\frac{330+72\sqrt{21}}{18}
$