9(-7n-6)n=7

Solution for 9(-7n-6)n=7 equation:

9(-7n-6)n=7

We move all terms to the left:

9(-7n-6)n-(7)=0

We multiply parentheses

-63n^2-54n-7=0

a = -63; b = -54; c = -7;
Δ = b2-4ac
Δ = -542-4·(-63)·(-7)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-24\sqrt{2}}{2*-63}=\frac{54-24\sqrt{2}}{-126}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+24\sqrt{2}}{2*-63}=\frac{54+24\sqrt{2}}{-126}
$