-30=n(3n+21)

Solution for -30=n(3n+21) equation:

-30=n(3n+21)

We move all terms to the left:

-30-(n(3n+21))=0


We calculate terms in parentheses: -(n(3n+21)), so:

n(3n+21)

We multiply parentheses

3n^2+21n

Back to the equation:

-(3n^2+21n)


We get rid of parentheses

-3n^2-21n-30=0

a = -3; b = -21; c = -30;
Δ = b2-4ac
Δ = -212-4·(-3)·(-30)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*-3}=\frac{12}{-6}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*-3}=\frac{30}{-6}
=-5
$