x+1/x=48

Solution for x+1/x=48 equation:

x+1/x=48

We move all terms to the left:

x+1/x-(48)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-48*x+1=0

We add all the numbers together, and all the variables

-48x+x*x+1=0

Wy multiply elements

x^2-48x+1=0

a = 1; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·1·1
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-10\sqrt{23}}{2*1}=\frac{48-10\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+10\sqrt{23}}{2*1}=\frac{48+10\sqrt{23}}{2}
$