x+18=11-12/x

Solution for x+18=11-12/x equation:

x+18=11-12/x

We move all terms to the left:

x+18-(11-12/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-(-12/x+11)+18=0

We get rid of parentheses

x+12/x-11+18=0

We multiply all the terms by the denominator


x*x-11*x+18*x+12=0

We add all the numbers together, and all the variables

7x+x*x+12=0

Wy multiply elements

x^2+7x+12=0

a = 1; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·1·12
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{-(7)-1}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*1}=\frac{-6}{2}
=-3
$