x+1/3x+2x=90

Solution for x+1/3x+2x=90 equation:

x+1/3x+2x=90

We move all terms to the left:

x+1/3x+2x-(90)=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-90=0

We multiply all the terms by the denominator


3x*3x-90*3x+1=0

Wy multiply elements

9x^2-270x+1=0

a = 9; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·9·1
Δ = 72864
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:

$\sqrt{\Delta}=\sqrt{72864}=\sqrt{144*506}=\sqrt{144}*\sqrt{506}=12\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-12\sqrt{506}}{2*9}=\frac{270-12\sqrt{506}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+12\sqrt{506}}{2*9}=\frac{270+12\sqrt{506}}{18}
$