5/6c+3=1/3c-8

Solution for 5/6c+3=1/3c-8 equation:

5/6c+3=1/3c-8

We move all terms to the left:

5/6c+3-(1/3c-8)=0


Domain of the equation: 6c!=0

c!=0/6

c!=0

c∈R



Domain of the equation: 3c-8)!=0

c∈R


We get rid of parentheses

5/6c-1/3c+8+3=0

We calculate fractions


15c/18c^2+(-6c)/18c^2+8+3=0

We add all the numbers together, and all the variables

15c/18c^2+(-6c)/18c^2+11=0

We multiply all the terms by the denominator


15c+(-6c)+11*18c^2=0

Wy multiply elements

198c^2+15c+(-6c)=0

We get rid of parentheses

198c^2+15c-6c=0

We add all the numbers together, and all the variables

198c^2+9c=0

a = 198; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·198·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*198}=\frac{-18}{396}
=-1/22
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*198}=\frac{0}{396}
=0
$