Y=3(2x-1)(x+8)

Solution for Y=3(2x-1)(x+8) equation:

=3(2Y-1)(Y+8)

We move all terms to the left:

-(3(2Y-1)(Y+8))=0

We multiply parentheses ..

-(3(+2Y^2+16Y-1Y-8))=0


We calculate terms in parentheses: -(3(+2Y^2+16Y-1Y-8)), so:

3(+2Y^2+16Y-1Y-8)

We multiply parentheses

6Y^2+48Y-3Y-24

We add all the numbers together, and all the variables

6Y^2+45Y-24

Back to the equation:

-(6Y^2+45Y-24)


We get rid of parentheses

-6Y^2-45Y+24=0

a = -6; b = -45; c = +24;
Δ = b2-4ac
Δ = -452-4·(-6)·24
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-51}{2*-6}=\frac{-6}{-12}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+51}{2*-6}=\frac{96}{-12}
=-8
$