X-1/3x-1=0

Solution for X-1/3x-1=0 equation:

X-1/3X-1=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-1*3X-1=0

Wy multiply elements

3X^2-3X-1=0

a = 3; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·3·(-1)
Δ = 21
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{-(-3)-\sqrt{21}}{2*3}=\frac{3-\sqrt{21}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*3}=\frac{3+\sqrt{21}}{6}
$