2x+7x=81/x

Solution for 2x+7x=81/x equation:

2x+7x=81/x

We move all terms to the left:

2x+7x-(81/x)=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+7x-(+81/x)=0

We add all the numbers together, and all the variables

9x-(+81/x)=0

We get rid of parentheses

9x-81/x=0

We multiply all the terms by the denominator


9x*x-81=0

Wy multiply elements

9x^2-81=0

a = 9; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·9·(-81)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*9}=\frac{-54}{18}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*9}=\frac{54}{18}
=3
$