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

Solution for (3n-9)(n+7)=0 equation:

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

We multiply parentheses ..

(+3n^2+21n-9n-63)=0

We get rid of parentheses

3n^2+21n-9n-63=0

We add all the numbers together, and all the variables

3n^2+12n-63=0

a = 3; b = 12; c = -63;
Δ = b2-4ac
Δ = 122-4·3·(-63)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-30}{2*3}=\frac{-42}{6}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+30}{2*3}=\frac{18}{6}
=3
$