Y=x(x-1)

Solution for Y=x(x-1) equation:

=Y(Y-1)

We move all terms to the left:

-(Y(Y-1))=0


We calculate terms in parentheses: -(Y(Y-1)), so:

Y(Y-1)

We multiply parentheses

Y^2-1Y

Back to the equation:

-(Y^2-1Y)


We get rid of parentheses

-Y^2+1Y=0

We add all the numbers together, and all the variables

-1Y^2+Y=0

a = -1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-1}=\frac{-2}{-2}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-1}=\frac{0}{-2}
=0
$