y(1-y)+2=5(2-y)

Solution for y(1-y)+2=5(2-y) equation:

y(1-y)+2=5(2-y)

We move all terms to the left:

y(1-y)+2-(5(2-y))=0

We add all the numbers together, and all the variables

y(-1y+1)-(5(-1y+2))+2=0

We multiply parentheses

-1y^2+y-(5(-1y+2))+2=0


We calculate terms in parentheses: -(5(-1y+2)), so:

5(-1y+2)

We multiply parentheses

-5y+10

Back to the equation:

-(-5y+10)


We get rid of parentheses

-1y^2+y+5y-10+2=0

We add all the numbers together, and all the variables

-1y^2+6y-8=0

a = -1; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·(-1)·(-8)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2}{2*-1}=\frac{-8}{-2}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*-1}=\frac{-4}{-2}
=+2
$