x+9,5=81/x

Solution for x+9,5=81/x equation:

x+9.5=81/x

We move all terms to the left:

x+9.5-(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

x-(+81/x)+9.5=0

We get rid of parentheses

x-81/x+9.5=0

We multiply all the terms by the denominator


x*x+(9.5)*x-81=0

We multiply parentheses

x*x+9.5x-81=0

Wy multiply elements

x^2+9.5x-81=0

a = 1; b = 9.5; c = -81;
Δ = b2-4ac
Δ = 9.52-4·1·(-81)
Δ = 414.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9.5)-\sqrt{414.25}}{2*1}=\frac{-9.5-\sqrt{414.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.5)+\sqrt{414.25}}{2*1}=\frac{-9.5+\sqrt{414.25}}{2}
$