(1/3.9x)+(1/x)=9

Solution for (1/3.9x)+(1/x)=9 equation:

(1/3.9x)+(1/x)=9

We move all terms to the left:

(1/3.9x)+(1/x)-(9)=0


Domain of the equation: 3.9x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3.9x)+(+1/x)-9=0

We get rid of parentheses

1/3.9x+1/x-9=0

We calculate fractions


x/(3.9x*x)+3x/(3.9x*x)-9=0

We add all the numbers together, and all the variables

x/(+3.9x*x)+3x/(+3.9x*x)-9=0

We multiply all the terms by the denominator


x+3x-9*(+3.9x*x)=0

We add all the numbers together, and all the variables

4x-9*(+3.9x*x)=0

We multiply parentheses

-27x^2+4x=0

a = -27; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-27)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-27}=\frac{-8}{-54}
=4/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-27}=\frac{0}{-54}
=0
$