(7n+2)(n-6)=0

Solution for (7n+2)(n-6)=0 equation:

(7n+2)(n-6)=0

We multiply parentheses ..

(+7n^2-42n+2n-12)=0

We get rid of parentheses

7n^2-42n+2n-12=0

We add all the numbers together, and all the variables

7n^2-40n-12=0

a = 7; b = -40; c = -12;
Δ = b2-4ac
Δ = -402-4·7·(-12)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-44}{2*7}=\frac{-4}{14}
=-2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+44}{2*7}=\frac{84}{14}
=6
$