x+1/3x+x-20=90

Solution for x+1/3x+x-20=90 equation:

x+1/3x+x-20=90

We move all terms to the left:

x+1/3x+x-20-(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

2x+1/3x-110=0

We multiply all the terms by the denominator


2x*3x-110*3x+1=0

Wy multiply elements

6x^2-330x+1=0

a = 6; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·6·1
Δ = 108876
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:

$\sqrt{\Delta}=\sqrt{108876}=\sqrt{4*27219}=\sqrt{4}*\sqrt{27219}=2\sqrt{27219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27219}}{2*6}=\frac{330-2\sqrt{27219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27219}}{2*6}=\frac{330+2\sqrt{27219}}{12}
$