D*p=(800-10p)*p

Solution for D*p=(800-10p)*p equation:

*D=(800-10D)*D

We move all terms to the left:

*D-((800-10D)*D)=0

We add all the numbers together, and all the variables

*D-((-10D+800)*D)=0

We add all the numbers together, and all the variables

D-((-10D+800)*D)=0


We calculate terms in parentheses: -((-10D+800)*D), so:

(-10D+800)*D

We multiply parentheses

-10D^2+800D

Back to the equation:

-(-10D^2+800D)


We get rid of parentheses

10D^2-800D+D=0

We add all the numbers together, and all the variables

10D^2-799D=0

a = 10; b = -799; c = 0;
Δ = b2-4ac
Δ = -7992-4·10·0
Δ = 638401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{638401}=799$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-799)-799}{2*10}=\frac{0}{20}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-799)+799}{2*10}=\frac{1598}{20}
=79+9/10
$