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

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

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


Domain of the equation: 3x^!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We calculate fractions


21x/63x^2+3x/63x^2-1=0

We multiply all the terms by the denominator


21x+3x-1*63x^2=0

We add all the numbers together, and all the variables

24x-1*63x^2=0

Wy multiply elements

-63x^2+24x=0

a = -63; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-63)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-63}=\frac{-48}{-126}
=8/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-63}=\frac{0}{-126}
=0
$