1800=6(3n2-900)

Solution for 1800=6(3n2-900) equation:

1800=6(3n^2-900)

We move all terms to the left:

1800-(6(3n^2-900))=0


We calculate terms in parentheses: -(6(3n^2-900)), so:

6(3n^2-900)

We multiply parentheses

18n^2-5400

Back to the equation:

-(18n^2-5400)


We get rid of parentheses

-18n^2+5400+1800=0

We add all the numbers together, and all the variables

-18n^2+7200=0

a = -18; b = 0; c = +7200;
Δ = b2-4ac
Δ = 02-4·(-18)·7200
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-720}{2*-18}=\frac{-720}{-36}
=+20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+720}{2*-18}=\frac{720}{-36}
=-20
$