3/x+x=24

Solution for 3/x+x=24 equation:

3/x+x=24

We move all terms to the left:

3/x+x-(24)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-24=0

We multiply all the terms by the denominator


x*x-24*x+3=0

We add all the numbers together, and all the variables

-24x+x*x+3=0

Wy multiply elements

x^2-24x+3=0

a = 1; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·1·3
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{141}}{2*1}=\frac{24-2\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{141}}{2*1}=\frac{24+2\sqrt{141}}{2}
$