5/x-7*x^-1-3+9=0

Solution for 5/x-7*x^-1-3+9=0 equation:

5/x-7x^-1-3+9=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-7x+5/x+5=0

We multiply all the terms by the denominator


-7x*x+5*x+5=0

We add all the numbers together, and all the variables

5x-7x*x+5=0

Wy multiply elements

-7x^2+5x+5=0

a = -7; b = 5; c = +5;
Δ = b2-4ac
Δ = 52-4·(-7)·5
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{165}}{2*-7}=\frac{-5-\sqrt{165}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{165}}{2*-7}=\frac{-5+\sqrt{165}}{-14}
$