4/3c*2-2=c

Solution for 4/3c*2-2=c equation:

4/3c*2-2=c

We move all terms to the left:

4/3c*2-2-(c)=0


Domain of the equation: 3c*2!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6c^2*2-12c*2+4=0

Wy multiply elements

-12c^2-24c+4=0

a = -12; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·(-12)·4
Δ = 768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{3}}{2*-12}=\frac{24-16\sqrt{3}}{-24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{3}}{2*-12}=\frac{24+16\sqrt{3}}{-24}
$