-9=x+2/x+12

Solution for -9=x+2/x+12 equation:

-9=x+2/x+12

We move all terms to the left:

-9-(x+2/x+12)=0


Domain of the equation: x+12)!=0

x∈R


We get rid of parentheses

-x-2/x-12-9=0

We multiply all the terms by the denominator


-x*x-12*x-9*x-2=0

We add all the numbers together, and all the variables

-21x-x*x-2=0

Wy multiply elements

-1x^2-21x-2=0

a = -1; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·(-1)·(-2)
Δ = 433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{433}}{2*-1}=\frac{21-\sqrt{433}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{433}}{2*-1}=\frac{21+\sqrt{433}}{-2}
$