100=(p-1)(200-40p)

Solution for 100=(p-1)(200-40p) equation:

100=(p-1)(200-40p)

We move all terms to the left:

100-((p-1)(200-40p))=0

We add all the numbers together, and all the variables

-((p-1)(-40p+200))+100=0

We multiply parentheses ..

-((-40p^2+200p+40p-200))+100=0


We calculate terms in parentheses: -((-40p^2+200p+40p-200)), so:

(-40p^2+200p+40p-200)

We get rid of parentheses

-40p^2+200p+40p-200

We add all the numbers together, and all the variables

-40p^2+240p-200

Back to the equation:

-(-40p^2+240p-200)


We get rid of parentheses

40p^2-240p+200+100=0

We add all the numbers together, and all the variables

40p^2-240p+300=0

a = 40; b = -240; c = +300;
Δ = b2-4ac
Δ = -2402-4·40·300
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-40\sqrt{6}}{2*40}=\frac{240-40\sqrt{6}}{80}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+40\sqrt{6}}{2*40}=\frac{240+40\sqrt{6}}{80}
$