c-60=2/3c

Solution for c-60=2/3c equation:

c-60=2/3c

We move all terms to the left:

c-60-(2/3c)=0


Domain of the equation: 3c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

c-(+2/3c)-60=0

We get rid of parentheses

c-2/3c-60=0

We multiply all the terms by the denominator


c*3c-60*3c-2=0

Wy multiply elements

3c^2-180c-2=0

a = 3; b = -180; c = -2;
Δ = b2-4ac
Δ = -1802-4·3·(-2)
Δ = 32424
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:

$\sqrt{\Delta}=\sqrt{32424}=\sqrt{4*8106}=\sqrt{4}*\sqrt{8106}=2\sqrt{8106}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8106}}{2*3}=\frac{180-2\sqrt{8106}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8106}}{2*3}=\frac{180+2\sqrt{8106}}{6}
$