6=25x(1-x)

Solution for 6=25x(1-x) equation:

6=25x(1-x)

We move all terms to the left:

6-(25x(1-x))=0

We add all the numbers together, and all the variables

-(25x(-1x+1))+6=0


We calculate terms in parentheses: -(25x(-1x+1)), so:

25x(-1x+1)

We multiply parentheses

-25x^2+25x

Back to the equation:

-(-25x^2+25x)


We get rid of parentheses

25x^2-25x+6=0

a = 25; b = -25; c = +6;
Δ = b2-4ac
Δ = -252-4·25·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5}{2*25}=\frac{20}{50}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5}{2*25}=\frac{30}{50}
=3/5
$