x+20/x=9

Solution for x+20/x=9 equation:

x+20/x=9

We move all terms to the left:

x+20/x-(9)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-9*x+20=0

We add all the numbers together, and all the variables

-9x+x*x+20=0

Wy multiply elements

x^2-9x+20=0

a = 1; b = -9; c = +20;
Δ = b2-4ac
Δ = -92-4·1·20
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*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*1}=\frac{10}{2}
=5
$