72/3x+72/x=32

Solution for 72/3x+72/x=32 equation:

72/3x+72/x=32

We move all terms to the left:

72/3x+72/x-(32)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


72x/3x^2+216x/3x^2-32=0

We multiply all the terms by the denominator


72x+216x-32*3x^2=0

We add all the numbers together, and all the variables

288x-32*3x^2=0

Wy multiply elements

-96x^2+288x=0

a = -96; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-96)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-96}=\frac{-576}{-192}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-96}=\frac{0}{-192}
=0
$