x+1/3x=30

Solution for x+1/3x=30 equation:

x+1/3x=30

We move all terms to the left:

x+1/3x-(30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-30*3x+1=0

Wy multiply elements

3x^2-90x+1=0

a = 3; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·3·1
Δ = 8088
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:

$\sqrt{\Delta}=\sqrt{8088}=\sqrt{4*2022}=\sqrt{4}*\sqrt{2022}=2\sqrt{2022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2022}}{2*3}=\frac{90-2\sqrt{2022}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2022}}{2*3}=\frac{90+2\sqrt{2022}}{6}
$