(7n+6)(n-5)=0

Solution for (7n+6)(n-5)=0 equation:

(7n+6)(n-5)=0

We multiply parentheses ..

(+7n^2-35n+6n-30)=0

We get rid of parentheses

7n^2-35n+6n-30=0

We add all the numbers together, and all the variables

7n^2-29n-30=0

a = 7; b = -29; c = -30;
Δ = b2-4ac
Δ = -292-4·7·(-30)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-41}{2*7}=\frac{-12}{14}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+41}{2*7}=\frac{70}{14}
=5
$