-3n(2n+1)=-5

Solution for -3n(2n+1)=-5 equation:

-3n(2n+1)=-5

We move all terms to the left:

-3n(2n+1)-(-5)=0

We add all the numbers together, and all the variables

-3n(2n+1)+5=0

We multiply parentheses

-6n^2-3n+5=0

a = -6; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-6)·5
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{129}}{2*-6}=\frac{3-\sqrt{129}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{129}}{2*-6}=\frac{3+\sqrt{129}}{-12}
$