x-(20/x)=-1

Solution for x-(20/x)=-1 equation:

x-(20/x)=-1

We move all terms to the left:

x-(20/x)-(-1)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+20/x)-(-1)=0

We add all the numbers together, and all the variables

x-(+20/x)+1=0

We get rid of parentheses

x-20/x+1=0

We multiply all the terms by the denominator


x*x+1*x-20=0

We add all the numbers together, and all the variables

x+x*x-20=0

Wy multiply elements

x^2+x-20=0

a = 1; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*1}=\frac{8}{2}
=4
$