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

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

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

We multiply parentheses ..

(+7n^2-3n+49n-21)=0

We get rid of parentheses

7n^2-3n+49n-21=0

We add all the numbers together, and all the variables

7n^2+46n-21=0

a = 7; b = 46; c = -21;
Δ = b2-4ac
Δ = 462-4·7·(-21)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-52}{2*7}=\frac{-98}{14}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+52}{2*7}=\frac{6}{14}
=3/7
$