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

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

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

We multiply parentheses ..

(+7n^2+3n-63n-27)=0

We get rid of parentheses

7n^2+3n-63n-27=0

We add all the numbers together, and all the variables

7n^2-60n-27=0

a = 7; b = -60; c = -27;
Δ = b2-4ac
Δ = -602-4·7·(-27)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-66}{2*7}=\frac{-6}{14}
=-3/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+66}{2*7}=\frac{126}{14}
=9
$