1/2c=6.c=

Solution for 1/2c=6.c= equation:

1/2c=6.c=

We move all terms to the left:

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


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2c-6.c=0

We multiply all the terms by the denominator


-(6.c)*2c+1=0

We add all the numbers together, and all the variables

-(+6.c)*2c+1=0

We multiply parentheses

-12c^2+1=0

a = -12; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-12)·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-12}=\frac{0-4\sqrt{3}}{-24}
=-\frac{4\sqrt{3}}{-24}
=-\frac{\sqrt{3}}{-6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-12}=\frac{0+4\sqrt{3}}{-24}
=\frac{4\sqrt{3}}{-24}
=\frac{\sqrt{3}}{-6}
$