X-(6/x)=5

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

X-(6/X)=5

We move all terms to the left:

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

We get rid of parentheses

X-6/X-5=0

We multiply all the terms by the denominator


X*X-5*X-6=0

We add all the numbers together, and all the variables

-5X+X*X-6=0

Wy multiply elements

X^2-5X-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$