(n-7)*3n=-9

Solution for (n-7)*3n=-9 equation:

(n-7)*3n=-9

We move all terms to the left:

(n-7)*3n-(-9)=0

We add all the numbers together, and all the variables

(n-7)*3n+9=0

We multiply parentheses

3n^2-21n+9=0

a = 3; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·3·9
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{37}}{2*3}=\frac{21-3\sqrt{37}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{37}}{2*3}=\frac{21+3\sqrt{37}}{6}
$