2(c+4)c=7

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

2(c+4)c=7

We move all terms to the left:

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

We multiply parentheses

2c^2+8c-7=0

a = 2; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·2·(-7)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{30}}{2*2}=\frac{-8-2\sqrt{30}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{30}}{2*2}=\frac{-8+2\sqrt{30}}{4}
$