2c(c-8)=30

Solution for 2c(c-8)=30 equation:

2c(c-8)=30

We move all terms to the left:

2c(c-8)-(30)=0

We multiply parentheses

2c^2-16c-30=0

a = 2; b = -16; c = -30;
Δ = b2-4ac
Δ = -162-4·2·(-30)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*2}=\frac{16-4\sqrt{31}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*2}=\frac{16+4\sqrt{31}}{4}
$