6x+12/x=-18

Solution for 6x+12/x=-18 equation:

6x+12/x=-18

We move all terms to the left:

6x+12/x-(-18)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6x+12/x+18=0

We multiply all the terms by the denominator


6x*x+18*x+12=0

We add all the numbers together, and all the variables

18x+6x*x+12=0

Wy multiply elements

6x^2+18x+12=0

a = 6; b = 18; c = +12;
Δ = b2-4ac
Δ = 182-4·6·12
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*6}=\frac{-12}{12}
=-1
$