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

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

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

We multiply parentheses ..

(+49n^2+35n-7n-5)=0

We get rid of parentheses

49n^2+35n-7n-5=0

We add all the numbers together, and all the variables

49n^2+28n-5=0

a = 49; b = 28; c = -5;
Δ = b2-4ac
Δ = 282-4·49·(-5)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-42}{2*49}=\frac{-70}{98}
=-5/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+42}{2*49}=\frac{14}{98}
=1/7
$