Y=-(x-1)(x-7)

Solution for Y=-(x-1)(x-7) equation:

=-(Y-1)(Y-7)

We move all terms to the left:

-(-(Y-1)(Y-7))=0

We multiply parentheses ..

-(-(+Y^2-7Y-1Y+7))=0


We calculate terms in parentheses: -(-(+Y^2-7Y-1Y+7)), so:

-(+Y^2-7Y-1Y+7)

We get rid of parentheses

-Y^2+7Y+1Y-7

We add all the numbers together, and all the variables

-1Y^2+8Y-7

Back to the equation:

-(-1Y^2+8Y-7)


We get rid of parentheses

1Y^2-8Y+7=0

We add all the numbers together, and all the variables

Y^2-8Y+7=0

a = 1; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·1·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*1}=\frac{2}{2}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*1}=\frac{14}{2}
=7
$