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

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

=(Y-7)(Y-1)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

Y^2-1Y-7Y+7

We add all the numbers together, and all the variables

Y^2-8Y+7

Back to the equation:

-(Y^2-8Y+7)


We get rid of parentheses

-Y^2+8Y-7=0

We add all the numbers together, and all the variables

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