1/x+x+2x+1=100

Solution for 1/x+x+2x+1=100 equation:

1/x+x+2x+1=100

We move all terms to the left:

1/x+x+2x+1-(100)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/x-99=0

We multiply all the terms by the denominator


3x*x-99*x+1=0

We add all the numbers together, and all the variables

-99x+3x*x+1=0

Wy multiply elements

3x^2-99x+1=0

a = 3; b = -99; c = +1;
Δ = b2-4ac
Δ = -992-4·3·1
Δ = 9789
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-\sqrt{9789}}{2*3}=\frac{99-\sqrt{9789}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9789}}{2*3}=\frac{99+\sqrt{9789}}{6}
$