(n-5)(7n-1)=0

Solution for (n-5)(7n-1)=0 equation:

(n-5)(7n-1)=0

We multiply parentheses ..

(+7n^2-1n-35n+5)=0

We get rid of parentheses

7n^2-1n-35n+5=0

We add all the numbers together, and all the variables

7n^2-36n+5=0

a = 7; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·7·5
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-34}{2*7}=\frac{2}{14}
=1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+34}{2*7}=\frac{70}{14}
=5
$