X-6=-5/x

Solution for X-6=-5/x equation:

X-6=-5/X

We move all terms to the left:

X-6-(-5/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We get rid of parentheses

X+5/X-6=0

We multiply all the terms by the denominator


X*X-6*X+5=0

We add all the numbers together, and all the variables

-6X+X*X+5=0

Wy multiply elements

X^2-6X+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$