-5=(x^2+6)/x

Solution for -5=(x^2+6)/x equation:

-5=(x^2+6)/x

We move all terms to the left:

-5-((x^2+6)/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-((x^2+6)-5*x)=0


We calculate terms in parentheses: -((x^2+6)-5*x), so:

(x^2+6)-5*x

We add all the numbers together, and all the variables

-5x+(x^2+6)

We get rid of parentheses

x^2-5x+6

Back to the equation:

-(x^2-5x+6)


We get rid of parentheses

-x^2+5x-6=0

We add all the numbers together, and all the variables

-1x^2+5x-6=0

a = -1; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·(-1)·(-6)
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{-(5)-1}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-1}=\frac{-4}{-2}
=+2
$