50-1/50000x=4x

Solution for 50-1/50000x=4x equation:

50-1/50000x=4x

We move all terms to the left:

50-1/50000x-(4x)=0


Domain of the equation: 50000x!=0

x!=0/50000

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-1/50000x+50=0

We multiply all the terms by the denominator


-4x*50000x+50*50000x-1=0

Wy multiply elements

-200000x^2+2500000x-1=0

a = -200000; b = 2500000; c = -1;
Δ = b2-4ac
Δ = 25000002-4·(-200000)·(-1)
Δ = 6249999200000
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:

$\sqrt{\Delta}=\sqrt{6249999200000}=\sqrt{160000*39062495}=\sqrt{160000}*\sqrt{39062495}=400\sqrt{39062495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2500000)-400\sqrt{39062495}}{2*-200000}=\frac{-2500000-400\sqrt{39062495}}{-400000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2500000)+400\sqrt{39062495}}{2*-200000}=\frac{-2500000+400\sqrt{39062495}}{-400000}
$