4c^2=2c+6

Solution for 4c^2=2c+6 equation:

4c^2=2c+6

We move all terms to the left:

4c^2-(2c+6)=0

We get rid of parentheses

4c^2-2c-6=0

a = 4; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·4·(-6)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*4}=\frac{-8}{8}
=-1
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*4}=\frac{12}{8}
=1+1/2
$