3x+1/3x+x=90

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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} $

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