x+1/3x=197

Solution for x+1/3x=197 equation:

x+1/3x=197

We move all terms to the left:

x+1/3x-(197)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-197*3x+1=0

Wy multiply elements

3x^2-591x+1=0

a = 3; b = -591; c = +1;
Δ = b2-4ac
Δ = -5912-4·3·1
Δ = 349269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-591)-\sqrt{349269}}{2*3}=\frac{591-\sqrt{349269}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-591)+\sqrt{349269}}{2*3}=\frac{591+\sqrt{349269}}{6}
$