72/x+18=x+18/x

Solution for 72/x+18=x+18/x equation:

72/x+18=x+18/x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

72/x-x-18/x+18=0

We multiply all the terms by the denominator


-x*x+18*x+72-18=0

We add all the numbers together, and all the variables

18x-x*x+54=0

Wy multiply elements

-1x^2+18x+54=0

a = -1; b = 18; c = +54;
Δ = b2-4ac
Δ = 182-4·(-1)·54
Δ = 540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{15}}{2*-1}=\frac{-18-6\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{15}}{2*-1}=\frac{-18+6\sqrt{15}}{-2}
$