(n-5)(6n+1)=0

Solution for (n-5)(6n+1)=0 equation:

(n-5)(6n+1)=0

We multiply parentheses ..

(+6n^2+n-30n-5)=0

We get rid of parentheses

6n^2+n-30n-5=0

We add all the numbers together, and all the variables

6n^2-29n-5=0

a = 6; b = -29; c = -5;
Δ = b2-4ac
Δ = -292-4·6·(-5)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-31}{2*6}=\frac{-2}{12}
=-1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+31}{2*6}=\frac{60}{12}
=5
$