Y=-2(x+3)(x-8)

Solution for Y=-2(x+3)(x-8) equation:

=-2(Y+3)(Y-8)

We move all terms to the left:

-(-2(Y+3)(Y-8))=0

We multiply parentheses ..

-(-2(+Y^2-8Y+3Y-24))=0


We calculate terms in parentheses: -(-2(+Y^2-8Y+3Y-24)), so:

-2(+Y^2-8Y+3Y-24)

We multiply parentheses

-2Y^2+16Y-6Y+48

We add all the numbers together, and all the variables

-2Y^2+10Y+48

Back to the equation:

-(-2Y^2+10Y+48)


We get rid of parentheses

2Y^2-10Y-48=0

a = 2; b = -10; c = -48;
Δ = b2-4ac
Δ = -102-4·2·(-48)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*2}=\frac{-12}{4}
=-3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*2}=\frac{32}{4}
=8
$