4c^2-8c-54=0

Solution for 4c^2-8c-54=0 equation:

4c^2-8c-54=0

a = 4; b = -8; c = -54;
Δ = b2-4ac
Δ = -82-4·4·(-54)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{58}}{2*4}=\frac{8-4\sqrt{58}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{58}}{2*4}=\frac{8+4\sqrt{58}}{8}
$