(n+24)(2n-3)=45n

Solution for (n+24)(2n-3)=45n equation:

(n+24)(2n-3)=45n

We move all terms to the left:

(n+24)(2n-3)-(45n)=0

We add all the numbers together, and all the variables

-45n+(n+24)(2n-3)=0

We multiply parentheses ..

(+2n^2-3n+48n-72)-45n=0

We get rid of parentheses

2n^2-3n+48n-45n-72=0

We add all the numbers together, and all the variables

2n^2-72=0

a = 2; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·2·(-72)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*2}=\frac{-24}{4}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*2}=\frac{24}{4}
=6
$