-1/4x+x=2000

Solution for -1/4x+x=2000 equation:

-1/4x+x=2000

We move all terms to the left:

-1/4x+x-(2000)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x-1/4x-2000=0

We multiply all the terms by the denominator


x*4x-2000*4x-1=0

Wy multiply elements

4x^2-8000x-1=0

a = 4; b = -8000; c = -1;
Δ = b2-4ac
Δ = -80002-4·4·(-1)
Δ = 64000016
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:

$\sqrt{\Delta}=\sqrt{64000016}=\sqrt{16*4000001}=\sqrt{16}*\sqrt{4000001}=4\sqrt{4000001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8000)-4\sqrt{4000001}}{2*4}=\frac{8000-4\sqrt{4000001}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8000)+4\sqrt{4000001}}{2*4}=\frac{8000+4\sqrt{4000001}}{8}
$