x+(2x+5)/x+6=2

Solution for x+(2x+5)/x+6=2 equation:

x+(2x+5)/x+6=2

We move all terms to the left:

x+(2x+5)/x+6-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+(2x+5)/x+4=0

We multiply all the terms by the denominator


x*x+(2x+5)+4*x=0

We add all the numbers together, and all the variables

4x+x*x+(2x+5)=0

Wy multiply elements

x^2+4x+(2x+5)=0

We get rid of parentheses

x^2+4x+2x+5=0

We add all the numbers together, and all the variables

x^2+6x+5=0

a = 1; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*1}=\frac{-2}{2}
=-1
$