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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3c^2*2-6c*2+5=0

Wy multiply elements

6c^2-12c+5=0

a = 6; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·6·5
Δ = 24
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:

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