-11+18/u=u-18

Solution for -11+18/u=u-18 equation:

-11+18/u=u-18

We move all terms to the left:

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


Domain of the equation: u!=0

u∈R


We get rid of parentheses

18/u-u+18-11=0

We multiply all the terms by the denominator


-u*u+18*u-11*u+18=0

We add all the numbers together, and all the variables

7u-u*u+18=0

Wy multiply elements

-1u^2+7u+18=0

a = -1; b = 7; c = +18;
Δ = b2-4ac
Δ = 72-4·(-1)·18
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-1}=\frac{-18}{-2}
=+9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-1}=\frac{4}{-2}
=-2
$