Y=-2(x+5)(x-8)

Solution for Y=-2(x+5)(x-8) equation:

=-2(Y+5)(Y-8)

We move all terms to the left:

-(-2(Y+5)(Y-8))=0

We multiply parentheses ..

-(-2(+Y^2-8Y+5Y-40))=0


We calculate terms in parentheses: -(-2(+Y^2-8Y+5Y-40)), so:

-2(+Y^2-8Y+5Y-40)

We multiply parentheses

-2Y^2+16Y-10Y+80

We add all the numbers together, and all the variables

-2Y^2+6Y+80

Back to the equation:

-(-2Y^2+6Y+80)


We get rid of parentheses

2Y^2-6Y-80=0

a = 2; b = -6; c = -80;
Δ = b2-4ac
Δ = -62-4·2·(-80)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-26}{2*2}=\frac{-20}{4}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+26}{2*2}=\frac{32}{4}
=8
$