x+1/3x=90

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

x+1/3x=90

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-270x+1=0

a = 3; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·3·1
Δ = 72888
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:

$\sqrt{\Delta}=\sqrt{72888}=\sqrt{4*18222}=\sqrt{4}*\sqrt{18222}=2\sqrt{18222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18222}}{2*3}=\frac{270-2\sqrt{18222}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18222}}{2*3}=\frac{270+2\sqrt{18222}}{6}
$