X+1/3x=40

Solution for X+1/3x=40 equation:

X+1/3X=40

We move all terms to the left:

X+1/3X-(40)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-40*3X+1=0

Wy multiply elements

3X^2-120X+1=0

a = 3; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·3·1
Δ = 14388
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:

$\sqrt{\Delta}=\sqrt{14388}=\sqrt{4*3597}=\sqrt{4}*\sqrt{3597}=2\sqrt{3597}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3597}}{2*3}=\frac{120-2\sqrt{3597}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3597}}{2*3}=\frac{120+2\sqrt{3597}}{6}
$