Y=-(x-4)(x-7)

Solution for Y=-(x-4)(x-7) equation:

=-(Y-4)(Y-7)

We move all terms to the left:

-(-(Y-4)(Y-7))=0

We multiply parentheses ..

-(-(+Y^2-7Y-4Y+28))=0


We calculate terms in parentheses: -(-(+Y^2-7Y-4Y+28)), so:

-(+Y^2-7Y-4Y+28)

We get rid of parentheses

-Y^2+7Y+4Y-28

We add all the numbers together, and all the variables

-1Y^2+11Y-28

Back to the equation:

-(-1Y^2+11Y-28)


We get rid of parentheses

1Y^2-11Y+28=0

We add all the numbers together, and all the variables

Y^2-11Y+28=0

a = 1; b = -11; c = +28;
Δ = b2-4ac
Δ = -112-4·1·28
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{-(-11)-3}{2*1}=\frac{8}{2}
=4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*1}=\frac{14}{2}
=7
$