18x-77=18/x

Solution for 18x-77=18/x equation:

18x-77=18/x

We move all terms to the left:

18x-77-(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

18x-(+18/x)-77=0

We get rid of parentheses

18x-18/x-77=0

We multiply all the terms by the denominator


18x*x-77*x-18=0

We add all the numbers together, and all the variables

-77x+18x*x-18=0

Wy multiply elements

18x^2-77x-18=0

a = 18; b = -77; c = -18;
Δ = b2-4ac
Δ = -772-4·18·(-18)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-85}{2*18}=\frac{-8}{36}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+85}{2*18}=\frac{162}{36}
=4+1/2
$