126=n(36+3n-3)

Solution for 126=n(36+3n-3) equation:

126=n(36+3n-3)

We move all terms to the left:

126-(n(36+3n-3))=0

We add all the numbers together, and all the variables

-(n(3n+33))+126=0


We calculate terms in parentheses: -(n(3n+33)), so:

n(3n+33)

We multiply parentheses

3n^2+33n

Back to the equation:

-(3n^2+33n)


We get rid of parentheses

-3n^2-33n+126=0

a = -3; b = -33; c = +126;
Δ = b2-4ac
Δ = -332-4·(-3)·126
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-51}{2*-3}=\frac{-18}{-6}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+51}{2*-3}=\frac{84}{-6}
=-14
$