9/2x-1/21=3/7x

Solution for 9/2x-1/21=3/7x equation:

9/2x-1/21=3/7x

We move all terms to the left:

9/2x-1/21-(3/7x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-(+3/7x)-1/21=0

We get rid of parentheses

9/2x-3/7x-1/21=0

We calculate fractions


(-98x^2)/588x^2+2646x/588x^2+(-252x)/588x^2=0

We multiply all the terms by the denominator


(-98x^2)+2646x+(-252x)=0

We get rid of parentheses

-98x^2+2646x-252x=0

We add all the numbers together, and all the variables

-98x^2+2394x=0

a = -98; b = 2394; c = 0;
Δ = b2-4ac
Δ = 23942-4·(-98)·0
Δ = 5731236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5731236}=2394$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2394)-2394}{2*-98}=\frac{-4788}{-196}
=24+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2394)+2394}{2*-98}=\frac{0}{-196}
=0
$