3x+1/3x+x=90

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

3x+1/3x+x=90

We move all terms to the left:

3x+1/3x+x-(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

4x+1/3x-90=0

We multiply all the terms by the denominator


4x*3x-90*3x+1=0

Wy multiply elements

12x^2-270x+1=0

a = 12; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·12·1
Δ = 72852
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:

$\sqrt{\Delta}=\sqrt{72852}=\sqrt{4*18213}=\sqrt{4}*\sqrt{18213}=2\sqrt{18213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18213}}{2*12}=\frac{270-2\sqrt{18213}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18213}}{2*12}=\frac{270+2\sqrt{18213}}{24}
$