2x-(36/x)=-6

Solution for 2x-(36/x)=-6 equation:

2x-(36/x)=-6

We move all terms to the left:

2x-(36/x)-(-6)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+36/x)-(-6)=0

We add all the numbers together, and all the variables

2x-(+36/x)+6=0

We get rid of parentheses

2x-36/x+6=0

We multiply all the terms by the denominator


2x*x+6*x-36=0

We add all the numbers together, and all the variables

6x+2x*x-36=0

Wy multiply elements

2x^2+6x-36=0

a = 2; b = 6; c = -36;
Δ = b2-4ac
Δ = 62-4·2·(-36)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*2}=\frac{12}{4}
=3
$