-3n(7n-7)=-39-6n

Solution for -3n(7n-7)=-39-6n equation:

-3n(7n-7)=-39-6n

We move all terms to the left:

-3n(7n-7)-(-39-6n)=0

We add all the numbers together, and all the variables

-3n(7n-7)-(-6n-39)=0

We multiply parentheses

-21n^2+21n-(-6n-39)=0

We get rid of parentheses

-21n^2+21n+6n+39=0

We add all the numbers together, and all the variables

-21n^2+27n+39=0

a = -21; b = 27; c = +39;
Δ = b2-4ac
Δ = 272-4·(-21)·39
Δ = 4005
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4005}=\sqrt{9*445}=\sqrt{9}*\sqrt{445}=3\sqrt{445}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{445}}{2*-21}=\frac{-27-3\sqrt{445}}{-42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{445}}{2*-21}=\frac{-27+3\sqrt{445}}{-42}
$