7(c+4)c=2

Solution for 7(c+4)c=2 equation:

7(c+4)c=2

We move all terms to the left:

7(c+4)c-(2)=0

We multiply parentheses

7c^2+28c-2=0

a = 7; b = 28; c = -2;
Δ = b2-4ac
Δ = 282-4·7·(-2)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{210}}{2*7}=\frac{-28-2\sqrt{210}}{14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{210}}{2*7}=\frac{-28+2\sqrt{210}}{14}
$