1/x=14/5x+9

Solution for 1/x=14/5x+9 equation:

1/x=14/5x+9

We move all terms to the left:

1/x-(14/5x+9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

1/x-14/5x-9=0

We calculate fractions


5x/5x^2+(-14x)/5x^2-9=0

We multiply all the terms by the denominator


5x+(-14x)-9*5x^2=0

Wy multiply elements

-45x^2+5x+(-14x)=0

We get rid of parentheses

-45x^2+5x-14x=0

We add all the numbers together, and all the variables

-45x^2-9x=0

a = -45; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-45)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-45}=\frac{18}{-90}
=-1/5
$