(2x+17)/(x+1)=x+5

Solution for (2x+17)/(x+1)=x+5 equation:

(2x+17)/(x+1)=x+5

We move all terms to the left:

(2x+17)/(x+1)-(x+5)=0


Domain of the equation: (x+1)!=0

We move all terms containing x to the left, all other terms to the right

x!=-1

x∈R


We get rid of parentheses

(2x+17)/(x+1)-x-5=0

We multiply all the terms by the denominator


(2x+17)-x*(x+1)-5*(x+1)=0

We multiply parentheses

-x^2+(2x+17)-x-5x-5=0

We get rid of parentheses

-x^2+2x-x-5x+17-5=0

We add all the numbers together, and all the variables

-1x^2-4x+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$