x+4/x+12=-10

Solution for x+4/x+12=-10 equation:

x+4/x+12=-10

We move all terms to the left:

x+4/x+12-(-10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+4/x+22=0

We multiply all the terms by the denominator


x*x+22*x+4=0

We add all the numbers together, and all the variables

22x+x*x+4=0

Wy multiply elements

x^2+22x+4=0

a = 1; b = 22; c = +4;
Δ = b2-4ac
Δ = 222-4·1·4
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{13}}{2*1}=\frac{-22-6\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{13}}{2*1}=\frac{-22+6\sqrt{13}}{2}
$