5p(1-p)=10(1-p)

Solution for 5p(1-p)=10(1-p) equation:

5p(1-p)=10(1-p)

We move all terms to the left:

5p(1-p)-(10(1-p))=0

We add all the numbers together, and all the variables

5p(-1p+1)-(10(-1p+1))=0

We multiply parentheses

-5p^2+5p-(10(-1p+1))=0


We calculate terms in parentheses: -(10(-1p+1)), so:

10(-1p+1)

We multiply parentheses

-10p+10

Back to the equation:

-(-10p+10)


We get rid of parentheses

-5p^2+5p+10p-10=0

We add all the numbers together, and all the variables

-5p^2+15p-10=0

a = -5; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·(-5)·(-10)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5}{2*-5}=\frac{-20}{-10}
=+2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*-5}=\frac{-10}{-10}
=1
$