8/3c-2=2/c-12

Solution for 8/3c-2=2/c-12 equation:

8/3c-2=2/c-12

We move all terms to the left:

8/3c-2-(2/c-12)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R



Domain of the equation: c-12)!=0

c∈R


We get rid of parentheses

8/3c-2/c+12-2=0

We calculate fractions


8c/3c^2+(-6c)/3c^2+12-2=0

We add all the numbers together, and all the variables

8c/3c^2+(-6c)/3c^2+10=0

We multiply all the terms by the denominator


8c+(-6c)+10*3c^2=0

Wy multiply elements

30c^2+8c+(-6c)=0

We get rid of parentheses

30c^2+8c-6c=0

We add all the numbers together, and all the variables

30c^2+2c=0

a = 30; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·30·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*30}=\frac{-4}{60}
=-1/15
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*30}=\frac{0}{60}
=0
$