1=(-6c^2+8c+6)/(-2)

Solution for 1=(-6c^2+8c+6)/(-2) equation:

1=(-6c^2+8c+6)/(-2)

We move all terms to the left:

1-((-6c^2+8c+6)/(-2))=0

We multiply all the terms by the denominator


-((-6c^2+8c+6)+1*(-2))=0


We calculate terms in parentheses: -((-6c^2+8c+6)+1*(-2)), so:

(-6c^2+8c+6)+1*(-2)

We add all the numbers together, and all the variables

(-6c^2+8c+6)-2

We get rid of parentheses

-6c^2+8c+6-2

We add all the numbers together, and all the variables

-6c^2+8c+4

Back to the equation:

-(-6c^2+8c+4)


We get rid of parentheses

6c^2-8c-4=0

a = 6; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·6·(-4)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*6}=\frac{8-4\sqrt{10}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*6}=\frac{8+4\sqrt{10}}{12}
$