1/2x+x+5x=100

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

1/2x+x+5x=100

We move all terms to the left:

1/2x+x+5x-(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

6x+1/2x-100=0

We multiply all the terms by the denominator


6x*2x-100*2x+1=0

Wy multiply elements

12x^2-200x+1=0

a = 12; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·12·1
Δ = 39952
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:

$\sqrt{\Delta}=\sqrt{39952}=\sqrt{16*2497}=\sqrt{16}*\sqrt{2497}=4\sqrt{2497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2497}}{2*12}=\frac{200-4\sqrt{2497}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2497}}{2*12}=\frac{200+4\sqrt{2497}}{24}
$