1/2x+x-5+x=100

Solution for 1/2x+x-5+x=100 equation:

1/2x+x-5+x=100

We move all terms to the left:

1/2x+x-5+x-(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-105=0

We multiply all the terms by the denominator


2x*2x-105*2x+1=0

Wy multiply elements

4x^2-210x+1=0

a = 4; b = -210; c = +1;
Δ = b2-4ac
Δ = -2102-4·4·1
Δ = 44084
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:

$\sqrt{\Delta}=\sqrt{44084}=\sqrt{4*11021}=\sqrt{4}*\sqrt{11021}=2\sqrt{11021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11021}}{2*4}=\frac{210-2\sqrt{11021}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11021}}{2*4}=\frac{210+2\sqrt{11021}}{8}
$