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

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

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

We move all terms to the left:

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


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R



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

c∈R


We get rid of parentheses

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

We calculate fractions


24c/6c^2+(-4c)/6c^2+12-2=0

We add all the numbers together, and all the variables

24c/6c^2+(-4c)/6c^2+10=0

We multiply all the terms by the denominator


24c+(-4c)+10*6c^2=0

Wy multiply elements

60c^2+24c+(-4c)=0

We get rid of parentheses

60c^2+24c-4c=0

We add all the numbers together, and all the variables

60c^2+20c=0

a = 60; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·60·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*60}=\frac{-40}{120}
=-1/3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*60}=\frac{0}{120}
=0
$