(-40+80p)(80-80p)=-120+160p

Solution for (-40+80p)(80-80p)=-120+160p equation:

(-40+80p)(80-80p)=-120+160p

We move all terms to the left:

(-40+80p)(80-80p)-(-120+160p)=0

We add all the numbers together, and all the variables

(80p-40)(-80p+80)-(160p-120)=0

We get rid of parentheses

(80p-40)(-80p+80)-160p+120=0

We multiply parentheses ..

(-6400p^2+6400p+3200p-3200)-160p+120=0

We get rid of parentheses

-6400p^2+6400p+3200p-160p-3200+120=0

We add all the numbers together, and all the variables

-6400p^2+9440p-3080=0

a = -6400; b = 9440; c = -3080;
Δ = b2-4ac
Δ = 94402-4·(-6400)·(-3080)
Δ = 10265600
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:

$\sqrt{\Delta}=\sqrt{10265600}=\sqrt{25600*401}=\sqrt{25600}*\sqrt{401}=160\sqrt{401}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9440)-160\sqrt{401}}{2*-6400}=\frac{-9440-160\sqrt{401}}{-12800}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9440)+160\sqrt{401}}{2*-6400}=\frac{-9440+160\sqrt{401}}{-12800}
$