1000^2x-5=1/100

Solution for 1000^2x-5=1/100 equation:

1000^2x-5=1/100

We move all terms to the left:

1000^2x-5-(1/100)=0

We add all the numbers together, and all the variables

1000^2x-5-(+1/100)=0

We get rid of parentheses

1000^2x-5-1/100=0

We multiply all the terms by the denominator


1000^2x*100-1-5*100=0

We add all the numbers together, and all the variables

1000^2x*100-501=0

Wy multiply elements

100000x^2-501=0

a = 100000; b = 0; c = -501;
Δ = b2-4ac
Δ = 02-4·100000·(-501)
Δ = 200400000
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:

$\sqrt{\Delta}=\sqrt{200400000}=\sqrt{40000*5010}=\sqrt{40000}*\sqrt{5010}=200\sqrt{5010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5010}}{2*100000}=\frac{0-200\sqrt{5010}}{200000}
=-\frac{200\sqrt{5010}}{200000}
=-\frac{\sqrt{5010}}{1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5010}}{2*100000}=\frac{0+200\sqrt{5010}}{200000}
=\frac{200\sqrt{5010}}{200000}
=\frac{\sqrt{5010}}{1000}
$