-20/x=x-9

Solution for -20/x=x-9 equation:

-20/x=x-9

We move all terms to the left:

-20/x-(x-9)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-20/x-x+9=0

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

-1x^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{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-1}=\frac{-8}{-2}
=+4
$