8c=c^2+c^2+6

Solution for 8c=c^2+c^2+6 equation:

8c=c^2+c^2+6

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·(-2)·(-6)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*-2}=\frac{-12}{-4}
=+3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*-2}=\frac{-4}{-4}
=1
$