15+(x-5/x)=30

Solution for 15+(x-5/x)=30 equation:

15+(x-5/x)=30

We move all terms to the left:

15+(x-5/x)-(30)=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)+15-30=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-5/x-15=0

We multiply all the terms by the denominator


x*x-15*x-5=0

We add all the numbers together, and all the variables

-15x+x*x-5=0

Wy multiply elements

x^2-15x-5=0

a = 1; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·1·(-5)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-7\sqrt{5}}{2*1}=\frac{15-7\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7\sqrt{5}}{2*1}=\frac{15+7\sqrt{5}}{2}
$