1/2x-5x=100

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

1/2x-5x=100

We move all terms to the left:

1/2x-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

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -10; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·(-10)·1
Δ = 40040
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:

$\sqrt{\Delta}=\sqrt{40040}=\sqrt{4*10010}=\sqrt{4}*\sqrt{10010}=2\sqrt{10010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{10010}}{2*-10}=\frac{200-2\sqrt{10010}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{10010}}{2*-10}=\frac{200+2\sqrt{10010}}{-20}
$