-9(n+4)=-5n(4n+36)

Solution for -9(n+4)=-5n(4n+36) equation:

-9(n+4)=-5n(4n+36)

We move all terms to the left:

-9(n+4)-(-5n(4n+36))=0

We multiply parentheses

-9n-(-5n(4n+36))-36=0


We calculate terms in parentheses: -(-5n(4n+36)), so:

-5n(4n+36)

We multiply parentheses

-20n^2-180n

Back to the equation:

-(-20n^2-180n)


We get rid of parentheses

20n^2+180n-9n-36=0

We add all the numbers together, and all the variables

20n^2+171n-36=0

a = 20; b = 171; c = -36;
Δ = b2-4ac
Δ = 1712-4·20·(-36)
Δ = 32121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32121}=\sqrt{9*3569}=\sqrt{9}*\sqrt{3569}=3\sqrt{3569}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-3\sqrt{3569}}{2*20}=\frac{-171-3\sqrt{3569}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+3\sqrt{3569}}{2*20}=\frac{-171+3\sqrt{3569}}{40}
$