2=x+8/x-5

Solution for 2=x+8/x-5 equation:

2=x+8/x-5

We move all terms to the left:

2-(x+8/x-5)=0


Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

-x-8/x+5+2=0

We multiply all the terms by the denominator


-x*x+5*x+2*x-8=0

We add all the numbers together, and all the variables

7x-x*x-8=0

Wy multiply elements

-1x^2+7x-8=0

a = -1; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·(-1)·(-8)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{17}}{2*-1}=\frac{-7-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-1}=\frac{-7+\sqrt{17}}{-2}
$