y(y-3)=2(1-y)

Solution for y(y-3)=2(1-y) equation:

y(y-3)=2(1-y)

We move all terms to the left:

y(y-3)-(2(1-y))=0

We add all the numbers together, and all the variables

y(y-3)-(2(-1y+1))=0

We multiply parentheses

y^2-3y-(2(-1y+1))=0


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

2(-1y+1)

We multiply parentheses

-2y+2

Back to the equation:

-(-2y+2)


We get rid of parentheses

y^2-3y+2y-2=0

We add all the numbers together, and all the variables

y^2-1y-2=0

a = 1; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·1·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*1}=\frac{-2}{2}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*1}=\frac{4}{2}
=2
$