(1/2*x)+(x)+(x-5)=100

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

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

We move all terms to the left:

(1/2x)+(x)+(x-5)-(100)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2x)+x+(x-5)-100=0

We add all the numbers together, and all the variables

x+(+1/2x)+(x-5)-100=0

We get rid of parentheses

x+1/2x+x-5-100=0

We multiply all the terms by the denominator


x*2x+x*2x-5*2x-100*2x+1=0

Wy multiply elements

2x^2+2x^2-10x-200x+1=0

We add all the numbers together, and all the variables

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}
$