5+8/x=x+7

Solution for 5+8/x=x+7 equation:

5+8/x=x+7

We move all terms to the left:

5+8/x-(x+7)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8/x-x-7+5=0

We multiply all the terms by the denominator


-x*x-7*x+5*x+8=0

We add all the numbers together, and all the variables

-2x-x*x+8=0

Wy multiply elements

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

a = -1; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-1}=\frac{8}{-2}
=-4
$