X-8=15/x

Solution for X-8=15/x equation:

X-8=15/X

We move all terms to the left:

X-8-(15/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-(+15/X)-8=0

We get rid of parentheses

X-15/X-8=0

We multiply all the terms by the denominator


X*X-8*X-15=0

We add all the numbers together, and all the variables

-8X+X*X-15=0

Wy multiply elements

X^2-8X-15=0

a = 1; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·1·(-15)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{31}}{2*1}=\frac{8-2\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{31}}{2*1}=\frac{8+2\sqrt{31}}{2}
$