(5n(n+9))-3=24

Solution for (5n(n+9))-3=24 equation:

(5n(n+9))-3=24

We move all terms to the left:

(5n(n+9))-3-(24)=0

We add all the numbers together, and all the variables

(5n(n+9))-27=0


We calculate terms in parentheses: +(5n(n+9)), so:

5n(n+9)

We multiply parentheses

5n^2+45n

Back to the equation:

+(5n^2+45n)


We get rid of parentheses

5n^2+45n-27=0

a = 5; b = 45; c = -27;
Δ = b2-4ac
Δ = 452-4·5·(-27)
Δ = 2565
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:

$\sqrt{\Delta}=\sqrt{2565}=\sqrt{9*285}=\sqrt{9}*\sqrt{285}=3\sqrt{285}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{285}}{2*5}=\frac{-45-3\sqrt{285}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{285}}{2*5}=\frac{-45+3\sqrt{285}}{10}
$