-9n^2-11n+92=-12n-3n^2

Solution for -9n^2-11n+92=-12n-3n^2 equation:

-9n^2-11n+92=-12n-3n^2

We move all terms to the left:

-9n^2-11n+92-(-12n-3n^2)=0

We get rid of parentheses

-9n^2+3n^2+12n-11n+92=0

We add all the numbers together, and all the variables

-6n^2+n+92=0

a = -6; b = 1; c = +92;
Δ = b2-4ac
Δ = 12-4·(-6)·92
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-47}{2*-6}=\frac{-48}{-12}
=+4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+47}{2*-6}=\frac{46}{-12}
=-3+5/6
$