9/x+9/5x=1

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

9/x+9/5x=1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


45x/5x^2+9x/5x^2-1=0

We multiply all the terms by the denominator


45x+9x-1*5x^2=0

We add all the numbers together, and all the variables

54x-1*5x^2=0

Wy multiply elements

-5x^2+54x=0

a = -5; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-5)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-5}=\frac{-108}{-10}
=10+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-5}=\frac{0}{-10}
=0
$