.47x=10/x

Solution for .47x=10/x equation:

.47x=10/x

We move all terms to the left:

.47x-(10/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.47x-(+10/x)=0

We get rid of parentheses

.47x-10/x=0

We multiply all the terms by the denominator


(.47x)*x-10=0

We add all the numbers together, and all the variables

(+.47x)*x-10=0

We multiply parentheses

x^2-10=0

a = 1; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·1·(-10)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*1}=\frac{0-2\sqrt{10}}{2}
=-\frac{2\sqrt{10}}{2}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*1}=\frac{0+2\sqrt{10}}{2}
=\frac{2\sqrt{10}}{2}
=\sqrt{10}
$