15n(n+9)=3(45+5n)

Solution for 15n(n+9)=3(45+5n) equation:

15n(n+9)=3(45+5n)

We move all terms to the left:

15n(n+9)-(3(45+5n))=0

We add all the numbers together, and all the variables

15n(n+9)-(3(5n+45))=0

We multiply parentheses

15n^2+135n-(3(5n+45))=0


We calculate terms in parentheses: -(3(5n+45)), so:

3(5n+45)

We multiply parentheses

15n+135

Back to the equation:

-(15n+135)


We get rid of parentheses

15n^2+135n-15n-135=0

We add all the numbers together, and all the variables

15n^2+120n-135=0

a = 15; b = 120; c = -135;
Δ = b2-4ac
Δ = 1202-4·15·(-135)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-150}{2*15}=\frac{-270}{30}
=-9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+150}{2*15}=\frac{30}{30}
=1
$