P=x(-1.20x+1844)-80(-1.20x+1844)

Solution for P=x(-1.20x+1844)-80(-1.20x+1844) equation:

=P(-1.20P+1844)-80(-1.20P+1844)

We move all terms to the left:

-(P(-1.20P+1844)-80(-1.20P+1844))=0

We add all the numbers together, and all the variables

-(P(-1.2P+1844)-80(-1.2P+1844))=0


We calculate terms in parentheses: -(P(-1.2P+1844)-80(-1.2P+1844)), so:

P(-1.2P+1844)-80(-1.2P+1844)

We multiply parentheses

-1P^2+1844P+80P-147520

We add all the numbers together, and all the variables

-1P^2+1924P-147520

Back to the equation:

-(-1P^2+1924P-147520)


We get rid of parentheses

1P^2-1924P+147520=0

We add all the numbers together, and all the variables

P^2-1924P+147520=0

a = 1; b = -1924; c = +147520;
Δ = b2-4ac
Δ = -19242-4·1·147520
Δ = 3111696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3111696}=1764$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1924)-1764}{2*1}=\frac{160}{2}
=80
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1924)+1764}{2*1}=\frac{3688}{2}
=1844
$