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

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

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

We move all terms to the left:

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


Domain of the equation: c!=0

c∈R



Domain of the equation: 3c-12)!=0

c∈R


We get rid of parentheses

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

We calculate fractions


24c/3c^2+(-2c)/3c^2+12-2=0

We add all the numbers together, and all the variables

24c/3c^2+(-2c)/3c^2+10=0

We multiply all the terms by the denominator


24c+(-2c)+10*3c^2=0

Wy multiply elements

30c^2+24c+(-2c)=0

We get rid of parentheses

30c^2+24c-2c=0

We add all the numbers together, and all the variables

30c^2+22c=0

a = 30; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·30·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*30}=\frac{-44}{60}
=-11/15
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*30}=\frac{0}{60}
=0
$