10-x=5/x

Solution for 10-x=5/x equation:

10-x=5/x

We move all terms to the left:

10-x-(5/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-(+5/x)+10=0

We add all the numbers together, and all the variables

-1x-(+5/x)+10=0

We get rid of parentheses

-1x-5/x+10=0

We multiply all the terms by the denominator


-1x*x+10*x-5=0

We add all the numbers together, and all the variables

10x-1x*x-5=0

Wy multiply elements

-1x^2+10x-5=0

a = -1; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·(-1)·(-5)
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{-(10)-4\sqrt{5}}{2*-1}=\frac{-10-4\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*-1}=\frac{-10+4\sqrt{5}}{-2}
$