6/x+6=x+5

Solution for 6/x+6=x+5 equation:

6/x+6=x+5

We move all terms to the left:

6/x+6-(x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6/x-x-5+6=0

We multiply all the terms by the denominator


-x*x-5*x+6*x+6=0

We add all the numbers together, and all the variables

x-x*x+6=0

Wy multiply elements

-1x^2+x+6=0

a = -1; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-1)·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-1}=\frac{4}{-2}
=-2
$