Y=(x-5)(x-17)

Solution for Y=(x-5)(x-17) equation:

=(Y-5)(Y-17)

We move all terms to the left:

-((Y-5)(Y-17))=0

We multiply parentheses ..

-((+Y^2-17Y-5Y+85))=0


We calculate terms in parentheses: -((+Y^2-17Y-5Y+85)), so:

(+Y^2-17Y-5Y+85)

We get rid of parentheses

Y^2-17Y-5Y+85

We add all the numbers together, and all the variables

Y^2-22Y+85

Back to the equation:

-(Y^2-22Y+85)


We get rid of parentheses

-Y^2+22Y-85=0

We add all the numbers together, and all the variables

-1Y^2+22Y-85=0

a = -1; b = 22; c = -85;
Δ = b2-4ac
Δ = 222-4·(-1)·(-85)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-12}{2*-1}=\frac{-34}{-2}
=+17
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+12}{2*-1}=\frac{-10}{-2}
=+5
$