15=5x+10/x

Solution for 15=5x+10/x equation:

15=5x+10/x

We move all terms to the left:

15-(5x+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

-(+5x+10/x)+15=0

We get rid of parentheses

-5x-10/x+15=0

We multiply all the terms by the denominator


-5x*x+15*x-10=0

We add all the numbers together, and all the variables

15x-5x*x-10=0

Wy multiply elements

-5x^2+15x-10=0

a = -5; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·(-5)·(-10)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*-5}=\frac{-10}{-10}
=1
$