x-1/4(x)=2,000

Solution for x-1/4(x)=2,000 equation:

x-1/4(x)=2.000

We move all terms to the left:

x-1/4(x)-(2.000)=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-2=0

We multiply all the terms by the denominator


x*4x-2*4x-1=0

Wy multiply elements

4x^2-8x-1=0

a = 4; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·4·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*4}=\frac{8-4\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*4}=\frac{8+4\sqrt{5}}{8}
$