6c+12=2/c+3

Solution for 6c+12=2/c+3 equation:

6c+12=2/c+3

We move all terms to the left:

6c+12-(2/c+3)=0


Domain of the equation: c+3)!=0

c∈R


We get rid of parentheses

6c-2/c-3+12=0

We multiply all the terms by the denominator


6c*c-3*c+12*c-2=0

We add all the numbers together, and all the variables

9c+6c*c-2=0

Wy multiply elements

6c^2+9c-2=0

a = 6; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·6·(-2)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{129}}{2*6}=\frac{-9-\sqrt{129}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*6}=\frac{-9+\sqrt{129}}{12}
$