Y=-2(x-5)(x+17)

Solution for Y=-2(x-5)(x+17) equation:

=-2(Y-5)(Y+17)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We multiply parentheses

-2Y^2-34Y+10Y+170

We add all the numbers together, and all the variables

-2Y^2-24Y+170

Back to the equation:

-(-2Y^2-24Y+170)


We get rid of parentheses

2Y^2+24Y-170=0

a = 2; b = 24; c = -170;
Δ = b2-4ac
Δ = 242-4·2·(-170)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-44}{2*2}=\frac{-68}{4}
=-17
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+44}{2*2}=\frac{20}{4}
=5
$