3/x+x=96

Solution for 3/x+x=96 equation:

3/x+x=96

We move all terms to the left:

3/x+x-(96)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-96=0

We multiply all the terms by the denominator


x*x-96*x+3=0

We add all the numbers together, and all the variables

-96x+x*x+3=0

Wy multiply elements

x^2-96x+3=0

a = 1; b = -96; c = +3;
Δ = b2-4ac
Δ = -962-4·1·3
Δ = 9204
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:

$\sqrt{\Delta}=\sqrt{9204}=\sqrt{4*2301}=\sqrt{4}*\sqrt{2301}=2\sqrt{2301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2301}}{2*1}=\frac{96-2\sqrt{2301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2301}}{2*1}=\frac{96+2\sqrt{2301}}{2}
$