x*2=10/x

Solution for x*2=10/x equation:

x*2=10/x

We move all terms to the left:

x*2-(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

x*2-(+10/x)=0

Wy multiply elements

2x-(+10/x)=0

We get rid of parentheses

2x-10/x=0

We multiply all the terms by the denominator


2x*x-10=0

Wy multiply elements

2x^2-10=0

a = 2; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·2·(-10)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*2}=\frac{0-4\sqrt{5}}{4}
=-\frac{4\sqrt{5}}{4}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*2}=\frac{0+4\sqrt{5}}{4}
=\frac{4\sqrt{5}}{4}
=\sqrt{5}
$