x+(12/x+1)=-9

Solution for x+(12/x+1)=-9 equation:

x+(12/x+1)=-9

We move all terms to the left:

x+(12/x+1)-(-9)=0


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

x∈R


We add all the numbers together, and all the variables

x+(12/x+1)+9=0

We get rid of parentheses

x+12/x+1+9=0

We multiply all the terms by the denominator


x*x+1*x+9*x+12=0

We add all the numbers together, and all the variables

10x+x*x+12=0

Wy multiply elements

x^2+10x+12=0

a = 1; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·1·12
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*1}=\frac{-10-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*1}=\frac{-10+2\sqrt{13}}{2}
$