x=11-18/x

Solution for x=11-18/x equation:

x=11-18/x

We move all terms to the left:

x-(11-18/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-(-18/x+11)=0

We get rid of parentheses

x+18/x-11=0

We multiply all the terms by the denominator


x*x-11*x+18=0

We add all the numbers together, and all the variables

-11x+x*x+18=0

Wy multiply elements

x^2-11x+18=0

a = 1; b = -11; c = +18;
Δ = b2-4ac
Δ = -112-4·1·18
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{-(-11)-7}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*1}=\frac{18}{2}
=9
$