50-1/2x=2x

Solution for 50-1/2x=2x equation:

50-1/2x=2x

We move all terms to the left:

50-1/2x-(2x)=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+50=0

We multiply all the terms by the denominator


-2x*2x+50*2x-1=0

Wy multiply elements

-4x^2+100x-1=0

a = -4; b = 100; c = -1;
Δ = b2-4ac
Δ = 1002-4·(-4)·(-1)
Δ = 9984
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:

$\sqrt{\Delta}=\sqrt{9984}=\sqrt{256*39}=\sqrt{256}*\sqrt{39}=16\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-16\sqrt{39}}{2*-4}=\frac{-100-16\sqrt{39}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+16\sqrt{39}}{2*-4}=\frac{-100+16\sqrt{39}}{-8}
$