(6n+1)(5n+4)=0

Solution for (6n+1)(5n+4)=0 equation:

(6n+1)(5n+4)=0

We multiply parentheses ..

(+30n^2+24n+5n+4)=0

We get rid of parentheses

30n^2+24n+5n+4=0

We add all the numbers together, and all the variables

30n^2+29n+4=0

a = 30; b = 29; c = +4;
Δ = b2-4ac
Δ = 292-4·30·4
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-19}{2*30}=\frac{-48}{60}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+19}{2*30}=\frac{-10}{60}
=-1/6
$