8/33c-2=2/3c-12

Solution for 8/33c-2=2/3c-12 equation:

8/33c-2=2/3c-12

We move all terms to the left:

8/33c-2-(2/3c-12)=0


Domain of the equation: 33c!=0

c!=0/33

c!=0

c∈R



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

c∈R


We get rid of parentheses

8/33c-2/3c+12-2=0

We calculate fractions


24c/99c^2+(-66c)/99c^2+12-2=0

We add all the numbers together, and all the variables

24c/99c^2+(-66c)/99c^2+10=0

We multiply all the terms by the denominator


24c+(-66c)+10*99c^2=0

Wy multiply elements

990c^2+24c+(-66c)=0

We get rid of parentheses

990c^2+24c-66c=0

We add all the numbers together, and all the variables

990c^2-42c=0

a = 990; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·990·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*990}=\frac{0}{1980}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*990}=\frac{84}{1980}
=7/165
$