X+1/3x=35

Solution for X+1/3x=35 equation:

X+1/3X=35

We move all terms to the left:

X+1/3X-(35)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-35*3X+1=0

Wy multiply elements

3X^2-105X+1=0

a = 3; b = -105; c = +1;
Δ = b2-4ac
Δ = -1052-4·3·1
Δ = 11013
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{-(-105)-\sqrt{11013}}{2*3}=\frac{105-\sqrt{11013}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11013}}{2*3}=\frac{105+\sqrt{11013}}{6}
$