-4n(-6n+1)=40+2n

Solution for -4n(-6n+1)=40+2n equation:

-4n(-6n+1)=40+2n

We move all terms to the left:

-4n(-6n+1)-(40+2n)=0

We add all the numbers together, and all the variables

-4n(-6n+1)-(2n+40)=0

We multiply parentheses

24n^2-4n-(2n+40)=0

We get rid of parentheses

24n^2-4n-2n-40=0

We add all the numbers together, and all the variables

24n^2-6n-40=0

a = 24; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·24·(-40)
Δ = 3876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3876}=\sqrt{4*969}=\sqrt{4}*\sqrt{969}=2\sqrt{969}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{969}}{2*24}=\frac{6-2\sqrt{969}}{48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{969}}{2*24}=\frac{6+2\sqrt{969}}{48}
$