10^2x-3=1/10000

Solution for 10^2x-3=1/10000 equation:

10^2x-3=1/10000

We move all terms to the left:

10^2x-3-(1/10000)=0

We add all the numbers together, and all the variables

10^2x-3-(+1/10000)=0

We get rid of parentheses

10^2x-3-1/10000=0

We multiply all the terms by the denominator


10^2x*10000-1-3*10000=0

We add all the numbers together, and all the variables

10^2x*10000-30001=0

Wy multiply elements

100000x^2-30001=0

a = 100000; b = 0; c = -30001;
Δ = b2-4ac
Δ = 02-4·100000·(-30001)
Δ = 12000400000
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:

$\sqrt{\Delta}=\sqrt{12000400000}=\sqrt{40000*300010}=\sqrt{40000}*\sqrt{300010}=200\sqrt{300010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{300010}}{2*100000}=\frac{0-200\sqrt{300010}}{200000}
=-\frac{200\sqrt{300010}}{200000}
=-\frac{\sqrt{300010}}{1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{300010}}{2*100000}=\frac{0+200\sqrt{300010}}{200000}
=\frac{200\sqrt{300010}}{200000}
=\frac{\sqrt{300010}}{1000}
$