6-3c=2-1/2c

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

6-3c=2-1/2c

We move all terms to the left:

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


Domain of the equation: 2c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6c^2-4c+12c+1=0

We add all the numbers together, and all the variables

-6c^2+8c+1=0

a = -6; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-6)·1
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*-6}=\frac{-8-2\sqrt{22}}{-12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*-6}=\frac{-8+2\sqrt{22}}{-12}
$