-6n(4n-5)=0

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

-6n(4n-5)=0

We multiply parentheses

-24n^2+30n=0

a = -24; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-24)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-24}=\frac{-60}{-48}
=1+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-24}=\frac{0}{-48}
=0
$