7(c-4)c=8

Solution for 7(c-4)c=8 equation:

7(c-4)c=8

We move all terms to the left:

7(c-4)c-(8)=0

We multiply parentheses

7c^2-28c-8=0

a = 7; b = -28; c = -8;
Δ = b2-4ac
Δ = -282-4·7·(-8)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12\sqrt{7}}{2*7}=\frac{28-12\sqrt{7}}{14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12\sqrt{7}}{2*7}=\frac{28+12\sqrt{7}}{14}
$