660=n/2+6n2-6n

Solution for 660=n/2+6n2-6n equation:

660=n/2+6n^2-6n

We move all terms to the left:

660-(n/2+6n^2-6n)=0


Domain of the equation: 2+6n^2-6n)!=0

We move all terms containing n to the left, all other terms to the right

6n^2-6n)!=-2

n∈R


We get rid of parentheses

-6n^2-n/2+6n+660=0

We multiply all the terms by the denominator


-6n^2*2-n+6n*2+660*2=0

We add all the numbers together, and all the variables

-6n^2*2-1n+6n*2+1320=0

Wy multiply elements

-12n^2-1n+12n+1320=0

We add all the numbers together, and all the variables

-12n^2+11n+1320=0

a = -12; b = 11; c = +1320;
Δ = b2-4ac
Δ = 112-4·(-12)·1320
Δ = 63481
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{-(11)-\sqrt{63481}}{2*-12}=\frac{-11-\sqrt{63481}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{63481}}{2*-12}=\frac{-11+\sqrt{63481}}{-24}
$