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

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

X+X+1/2X+1=100

We move all terms to the left:

X+X+1/2X+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

2X+1/2X-99=0

We multiply all the terms by the denominator


2X*2X-99*2X+1=0

Wy multiply elements

4X^2-198X+1=0

a = 4; b = -198; c = +1;
Δ = b2-4ac
Δ = -1982-4·4·1
Δ = 39188
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:

$\sqrt{\Delta}=\sqrt{39188}=\sqrt{4*9797}=\sqrt{4}*\sqrt{9797}=2\sqrt{9797}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9797}}{2*4}=\frac{198-2\sqrt{9797}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9797}}{2*4}=\frac{198+2\sqrt{9797}}{8}
$