P=7.5n(2.25n+15)

Solution for P=7.5n(2.25n+15) equation:

=7.5P(2.25P+15)

We move all terms to the left:

-(7.5P(2.25P+15))=0


We calculate terms in parentheses: -(7.5P(2.25P+15)), so:

7.5P(2.25P+15)

We multiply parentheses

14P^2+105P

Back to the equation:

-(14P^2+105P)


We get rid of parentheses

-14P^2-105P=0

a = -14; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·(-14)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*-14}=\frac{0}{-28}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*-14}=\frac{210}{-28}
=-7+1/2
$