(1/x*10^-3)=25

Solution for (1/x*10^-3)=25 equation:

(1/x*10^-3)=25

We move all terms to the left:

(1/x*10^-3)-(25)=0


Domain of the equation: x*10^-3)!=0

x∈R


We get rid of parentheses

1/x*10^-3-25=0

We multiply all the terms by the denominator


-3*x*10^-25*x*10^+1=0

Wy multiply elements

-30x^2*1-250x^2*1+1=0

Wy multiply elements

-30x^2-250x^2+1=0

We add all the numbers together, and all the variables

-280x^2+1=0

a = -280; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-280)·1
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{70}}{2*-280}=\frac{0-4\sqrt{70}}{-560}
=-\frac{4\sqrt{70}}{-560}
=-\frac{\sqrt{70}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{70}}{2*-280}=\frac{0+4\sqrt{70}}{-560}
=\frac{4\sqrt{70}}{-560}
=\frac{\sqrt{70}}{-140}
$