72/x+x=18

Solution for 72/x+x=18 equation:

72/x+x=18

We move all terms to the left:

72/x+x-(18)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+72/x-18=0

We multiply all the terms by the denominator


x*x-18*x+72=0

We add all the numbers together, and all the variables

-18x+x*x+72=0

Wy multiply elements

x^2-18x+72=0

a = 1; b = -18; c = +72;
Δ = b2-4ac
Δ = -182-4·1·72
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*1}=\frac{24}{2}
=12
$