0=4x+5/x-9

Solution for 0=4x+5/x-9 equation:

0=4x+5/x-9

We move all terms to the left:

0-(4x+5/x-9)=0


Domain of the equation: x-9)!=0

x∈R


We add all the numbers together, and all the variables

-(4x+5/x-9)=0

We get rid of parentheses

-4x-5/x+9=0

We multiply all the terms by the denominator


-4x*x+9*x-5=0

We add all the numbers together, and all the variables

9x-4x*x-5=0

Wy multiply elements

-4x^2+9x-5=0

a = -4; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-4)·(-5)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-4}=\frac{-8}{-8}
=1
$