0.45/x=2.05x

Solution for 0.45/x=2.05x equation:

0.45/x=2.05x

We move all terms to the left:

0.45/x-(2.05x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

0.45/x-(+2.05x)=0

We get rid of parentheses

0.45/x-2.05x=0

We multiply all the terms by the denominator


-(2.05x)*x+0.45=0

We add all the numbers together, and all the variables

-(+2.05x)*x+0.45=0

We multiply parentheses

-2x^2+0.45=0

a = -2; b = 0; c = +0.45;
Δ = b2-4ac
Δ = 02-4·(-2)·0.45
Δ = 3.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{3.6}}{2*-2}=\frac{0-\sqrt{3.6}}{-4}
=-\frac{\sqrt{}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{3.6}}{2*-2}=\frac{0+\sqrt{3.6}}{-4}
=\frac{\sqrt{}}{-4}
$