X+(1/3x)=49

Solution for X+(1/3x)=49 equation:

X+(1/3X)=49

We move all terms to the left:

X+(1/3X)-(49)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+1/3X)-49=0

We get rid of parentheses

X+1/3X-49=0

We multiply all the terms by the denominator


X*3X-49*3X+1=0

Wy multiply elements

3X^2-147X+1=0

a = 3; b = -147; c = +1;
Δ = b2-4ac
Δ = -1472-4·3·1
Δ = 21597
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{-(-147)-\sqrt{21597}}{2*3}=\frac{147-\sqrt{21597}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+\sqrt{21597}}{2*3}=\frac{147+\sqrt{21597}}{6}
$