3-5e-6=-2/5e-3

Solution for 3-5e-6=-2/5e-3 equation:

3-5e-6=-2/5e-3

We move all terms to the left:

3-5e-6-(-2/5e-3)=0


Domain of the equation: 5e-3)!=0

e∈R


We add all the numbers together, and all the variables

-5e-(-2/5e-3)-3=0

We get rid of parentheses

-5e+2/5e+3-3=0

We multiply all the terms by the denominator


-5e*5e+3*5e-3*5e+2=0

Wy multiply elements

-25e^2+15e-15e+2=0

We add all the numbers together, and all the variables

-25e^2+2=0

a = -25; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-25)·2
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*-25}=\frac{0-10\sqrt{2}}{-50}
=-\frac{10\sqrt{2}}{-50}
=-\frac{\sqrt{2}}{-5}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-25}=\frac{0+10\sqrt{2}}{-50}
=\frac{10\sqrt{2}}{-50}
=\frac{\sqrt{2}}{-5}
$