N-5n+12=3n2

Solution for N-5n+12=3n2 equation:

-5N+12=3N^2

We move all terms to the left:

-5N+12-(3N^2)=0

determiningTheFunctionDomain
-3N^2-5N+12=0

a = -3; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-3)·12
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-3}=\frac{18}{-6}
=-3
$