1x+1/4x=200,000

Solution for 1x+1/4x=200,000 equation:

1x+1/4x=200.000

We move all terms to the left:

1x+1/4x-(200.000)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1x+1/4x-200=0

We add all the numbers together, and all the variables

x+1/4x-200=0

We multiply all the terms by the denominator


x*4x-200*4x+1=0

Wy multiply elements

4x^2-800x+1=0

a = 4; b = -800; c = +1;
Δ = b2-4ac
Δ = -8002-4·4·1
Δ = 639984
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:

$\sqrt{\Delta}=\sqrt{639984}=\sqrt{16*39999}=\sqrt{16}*\sqrt{39999}=4\sqrt{39999}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-4\sqrt{39999}}{2*4}=\frac{800-4\sqrt{39999}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+4\sqrt{39999}}{2*4}=\frac{800+4\sqrt{39999}}{8}
$