Y=(x-7)(x+3)

Solution for Y=(x-7)(x+3) equation:

=(Y-7)(Y+3)

We move all terms to the left:

-((Y-7)(Y+3))=0

We multiply parentheses ..

-((+Y^2+3Y-7Y-21))=0


We calculate terms in parentheses: -((+Y^2+3Y-7Y-21)), so:

(+Y^2+3Y-7Y-21)

We get rid of parentheses

Y^2+3Y-7Y-21

We add all the numbers together, and all the variables

Y^2-4Y-21

Back to the equation:

-(Y^2-4Y-21)


We get rid of parentheses

-Y^2+4Y+21=0

We add all the numbers together, and all the variables

-1Y^2+4Y+21=0

a = -1; b = 4; c = +21;
Δ = b2-4ac
Δ = 42-4·(-1)·21
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*-1}=\frac{-14}{-2}
=+7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*-1}=\frac{6}{-2}
=-3
$