x+1/3x=42

Solution for x+1/3x=42 equation:

x+1/3x=42

We move all terms to the left:

x+1/3x-(42)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-42*3x+1=0

Wy multiply elements

3x^2-126x+1=0

a = 3; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·3·1
Δ = 15864
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:

$\sqrt{\Delta}=\sqrt{15864}=\sqrt{4*3966}=\sqrt{4}*\sqrt{3966}=2\sqrt{3966}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3966}}{2*3}=\frac{126-2\sqrt{3966}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3966}}{2*3}=\frac{126+2\sqrt{3966}}{6}
$