-8c(c-6)=-21

Solution for -8c(c-6)=-21 equation:

-8c(c-6)=-21

We move all terms to the left:

-8c(c-6)-(-21)=0

We add all the numbers together, and all the variables

-8c(c-6)+21=0

We multiply parentheses

-8c^2+48c+21=0

a = -8; b = 48; c = +21;
Δ = b2-4ac
Δ = 482-4·(-8)·21
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{186}}{2*-8}=\frac{-48-4\sqrt{186}}{-16}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{186}}{2*-8}=\frac{-48+4\sqrt{186}}{-16}
$