x-8/x=-1

Solution for x-8/x=-1 equation:

x-8/x=-1

We move all terms to the left:

x-8/x-(-1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-8/x+1=0

We multiply all the terms by the denominator


x*x+1*x-8=0

We add all the numbers together, and all the variables

x+x*x-8=0

Wy multiply elements

x^2+x-8=0

a = 1; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·1·(-8)
Δ = 33
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{-(1)-\sqrt{33}}{2*1}=\frac{-1-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*1}=\frac{-1+\sqrt{33}}{2}
$