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

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

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

We move all terms to the left:

x+x+x+1/2x-(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

3x+1/2x-100=0

We multiply all the terms by the denominator


3x*2x-100*2x+1=0

Wy multiply elements

6x^2-200x+1=0

a = 6; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·6·1
Δ = 39976
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:

$\sqrt{\Delta}=\sqrt{39976}=\sqrt{4*9994}=\sqrt{4}*\sqrt{9994}=2\sqrt{9994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{9994}}{2*6}=\frac{200-2\sqrt{9994}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{9994}}{2*6}=\frac{200+2\sqrt{9994}}{12}
$