4/x+12/(x+3)=-13

Solution for 4/x+12/(x+3)=-13 equation:

4/x+12/(x+3)=-13

We move all terms to the left:

4/x+12/(x+3)-(-13)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+3)!=0

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

x!=-3

x∈R


We add all the numbers together, and all the variables

4/x+12/(x+3)+13=0

We calculate fractions


(4x+12)/(x^2+3x)+12x/(x^2+3x)+13=0

We multiply all the terms by the denominator


(4x+12)+12x+13*(x^2+3x)=0

We add all the numbers together, and all the variables

12x+(4x+12)+13*(x^2+3x)=0

We multiply parentheses

13x^2+12x+(4x+12)+39x=0

We get rid of parentheses

13x^2+12x+4x+39x+12=0

We add all the numbers together, and all the variables

13x^2+55x+12=0

a = 13; b = 55; c = +12;
Δ = b2-4ac
Δ = 552-4·13·12
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-49}{2*13}=\frac{-104}{26}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+49}{2*13}=\frac{-6}{26}
=-3/13
$