9x^2/21x+7-1/21x+7+1/x=9x^2/21x

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

9x^2/21x+7-1/21x+7+1/x=9x^2/21x

We move all terms to the left:

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


Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R



Domain of the equation: x!=0

x∈R



Domain of the equation: 21x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x^2/21x-1/21x+1/x-(9x^2/21x)+14=0

We get rid of parentheses

9x^2/21x-9x^2/21x-1/21x+1/x+14=0

We calculate fractions


(-x)/21x^2+21x/21x^2+14=0

We add all the numbers together, and all the variables

(-1x)/21x^2+21x/21x^2+14=0

We multiply all the terms by the denominator


(-1x)+21x+14*21x^2=0

We add all the numbers together, and all the variables

21x+(-1x)+14*21x^2=0

Wy multiply elements

294x^2+21x+(-1x)=0

We get rid of parentheses

294x^2+21x-1x=0

We add all the numbers together, and all the variables

294x^2+20x=0

a = 294; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·294·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*294}=\frac{-40}{588}
=-10/147
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*294}=\frac{0}{588}
=0
$