(65+12n)n=45

Solution for (65+12n)n=45 equation:

(65+12n)n=45

We move all terms to the left:

(65+12n)n-(45)=0

We add all the numbers together, and all the variables

(12n+65)n-45=0

We multiply parentheses

12n^2+65n-45=0

a = 12; b = 65; c = -45;
Δ = b2-4ac
Δ = 652-4·12·(-45)
Δ = 6385
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{-(65)-\sqrt{6385}}{2*12}=\frac{-65-\sqrt{6385}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{6385}}{2*12}=\frac{-65+\sqrt{6385}}{24}
$