1/x+1/x+9=17/9x+21

Solution for 1/x+1/x+9=17/9x+21 equation:

1/x+1/x+9=17/9x+21

We move all terms to the left:

1/x+1/x+9-(17/9x+21)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x+21)!=0

x∈R


We get rid of parentheses

1/x+1/x-17/9x-21+9=0

We calculate fractions


(9x+1)/9x^2+(-17x)/9x^2-21+9=0

We add all the numbers together, and all the variables

(9x+1)/9x^2+(-17x)/9x^2-12=0

We multiply all the terms by the denominator


(9x+1)+(-17x)-12*9x^2=0

Wy multiply elements

-108x^2+(9x+1)+(-17x)=0

We get rid of parentheses

-108x^2+9x-17x+1=0

We add all the numbers together, and all the variables

-108x^2-8x+1=0

a = -108; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-108)·1
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{31}}{2*-108}=\frac{8-4\sqrt{31}}{-216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{31}}{2*-108}=\frac{8+4\sqrt{31}}{-216}
$