x+18/x-18=5

Solution for x+18/x-18=5 equation:

x+18/x-18=5

We move all terms to the left:

x+18/x-18-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+18/x-23=0

We multiply all the terms by the denominator


x*x-23*x+18=0

We add all the numbers together, and all the variables

-23x+x*x+18=0

Wy multiply elements

x^2-23x+18=0

a = 1; b = -23; c = +18;
Δ = b2-4ac
Δ = -232-4·1·18
Δ = 457
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{-(-23)-\sqrt{457}}{2*1}=\frac{23-\sqrt{457}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{457}}{2*1}=\frac{23+\sqrt{457}}{2}
$