4/3c=c+2

Solution for 4/3c=c+2 equation:

4/3c=c+2

We move all terms to the left:

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


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We get rid of parentheses

4/3c-c-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3c^2-6c+4=0

a = -3; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-3)·4
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-3}=\frac{6-2\sqrt{21}}{-6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-3}=\frac{6+2\sqrt{21}}{-6}
$