X+x1/2x+1=100

Solution for X+x1/2x+1=100 equation:

X+X1/2X+1=100

We move all terms to the left:

X+X1/2X+1-(100)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+X1/2X-99=0

We multiply all the terms by the denominator


X*2X+X1-99*2X=0

We add all the numbers together, and all the variables

X+X*2X-99*2X=0

Wy multiply elements

2X^2+X-198X=0

We add all the numbers together, and all the variables

2X^2-197X=0

a = 2; b = -197; c = 0;
Δ = b2-4ac
Δ = -1972-4·2·0
Δ = 38809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38809}=197$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-197)-197}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-197)+197}{2*2}=\frac{394}{4}
=98+1/2
$