Y=(-x-9)(x-7)

Solution for Y=(-x-9)(x-7) equation:

=(-Y-9)(Y-7)

We move all terms to the left:

-((-Y-9)(Y-7))=0

We add all the numbers together, and all the variables

-((-1Y-9)(Y-7))=0

We multiply parentheses ..

-((-1Y^2+7Y-9Y+63))=0


We calculate terms in parentheses: -((-1Y^2+7Y-9Y+63)), so:

(-1Y^2+7Y-9Y+63)

We get rid of parentheses

-1Y^2+7Y-9Y+63

We add all the numbers together, and all the variables

-1Y^2-2Y+63

Back to the equation:

-(-1Y^2-2Y+63)


We get rid of parentheses

1Y^2+2Y-63=0

We add all the numbers together, and all the variables

Y^2+2Y-63=0

a = 1; b = 2; c = -63;
Δ = b2-4ac
Δ = 22-4·1·(-63)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*1}=\frac{-18}{2}
=-9
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*1}=\frac{14}{2}
=7
$