X-1/3x=6.2

Solution for X-1/3x=6.2 equation:

X-1/3X=6.2

We move all terms to the left:

X-1/3X-(6.2)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-1/3X-6.2=0

We multiply all the terms by the denominator


X*3X-(6.2)*3X-1=0

We multiply parentheses

X*3X-18.6X-1=0

Wy multiply elements

3X^2-18.6X-1=0

a = 3; b = -18.6; c = -1;
Δ = b2-4ac
Δ = -18.62-4·3·(-1)
Δ = 357.96
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{-(-18.6)-\sqrt{357.96}}{2*3}=\frac{18.6-\sqrt{357.96}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.6)+\sqrt{357.96}}{2*3}=\frac{18.6+\sqrt{357.96}}{6}
$