5/x=10/9x+1

Solution for 5/x=10/9x+1 equation:

5/x=10/9x+1

We move all terms to the left:

5/x-(10/9x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x+1)!=0

x∈R


We get rid of parentheses

5/x-10/9x-1=0

We calculate fractions


45x/9x^2+(-10x)/9x^2-1=0

We multiply all the terms by the denominator


45x+(-10x)-1*9x^2=0

Wy multiply elements

-9x^2+45x+(-10x)=0

We get rid of parentheses

-9x^2+45x-10x=0

We add all the numbers together, and all the variables

-9x^2+35x=0

a = -9; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-9)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-9}=\frac{-70}{-18}
=3+8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-9}=\frac{0}{-18}
=0
$