X+2x+1/3x=88

Solution for X+2x+1/3x=88 equation:

X+2X+1/3X=88

We move all terms to the left:

X+2X+1/3X-(88)=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-88=0

We multiply all the terms by the denominator


3X*3X-88*3X+1=0

Wy multiply elements

9X^2-264X+1=0

a = 9; b = -264; c = +1;
Δ = b2-4ac
Δ = -2642-4·9·1
Δ = 69660
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:

$\sqrt{\Delta}=\sqrt{69660}=\sqrt{324*215}=\sqrt{324}*\sqrt{215}=18\sqrt{215}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-18\sqrt{215}}{2*9}=\frac{264-18\sqrt{215}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+18\sqrt{215}}{2*9}=\frac{264+18\sqrt{215}}{18}
$