10x+(15/x)=40

Solution for 10x+(15/x)=40 equation:

10x+(15/x)=40

We move all terms to the left:

10x+(15/x)-(40)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x+(+15/x)-40=0

We get rid of parentheses

10x+15/x-40=0

We multiply all the terms by the denominator


10x*x-40*x+15=0

We add all the numbers together, and all the variables

-40x+10x*x+15=0

Wy multiply elements

10x^2-40x+15=0

a = 10; b = -40; c = +15;
Δ = b2-4ac
Δ = -402-4·10·15
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{10}}{2*10}=\frac{40-10\sqrt{10}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{10}}{2*10}=\frac{40+10\sqrt{10}}{20}
$