7c(c-12)=-21

Solution for 7c(c-12)=-21 equation:

7c(c-12)=-21

We move all terms to the left:

7c(c-12)-(-21)=0

We add all the numbers together, and all the variables

7c(c-12)+21=0

We multiply parentheses

7c^2-84c+21=0

a = 7; b = -84; c = +21;
Δ = b2-4ac
Δ = -842-4·7·21
Δ = 6468
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:

$\sqrt{\Delta}=\sqrt{6468}=\sqrt{196*33}=\sqrt{196}*\sqrt{33}=14\sqrt{33}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-14\sqrt{33}}{2*7}=\frac{84-14\sqrt{33}}{14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+14\sqrt{33}}{2*7}=\frac{84+14\sqrt{33}}{14}
$