6-4c=2/3c-1

Solution for 6-4c=2/3c-1 equation:

6-4c=2/3c-1

We move all terms to the left:

6-4c-(2/3c-1)=0


Domain of the equation: 3c-1)!=0

c∈R


We get rid of parentheses

-4c-2/3c+1+6=0

We multiply all the terms by the denominator


-4c*3c+1*3c+6*3c-2=0

Wy multiply elements

-12c^2+3c+18c-2=0

We add all the numbers together, and all the variables

-12c^2+21c-2=0

a = -12; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-12)·(-2)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{345}}{2*-12}=\frac{-21-\sqrt{345}}{-24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{345}}{2*-12}=\frac{-21+\sqrt{345}}{-24}
$