1/x-3+1/3x-21=0

Solution for 1/x-3+1/3x-21=0 equation:

1/x-3+1/3x-21=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/3x-24=0

We calculate fractions


3x/3x^2+x/3x^2-24=0

We multiply all the terms by the denominator


3x+x-24*3x^2=0

We add all the numbers together, and all the variables

4x-24*3x^2=0

Wy multiply elements

-72x^2+4x=0

a = -72; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-72)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-72}=\frac{-8}{-144}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-72}=\frac{0}{-144}
=0
$