Y=6(2x+3)(3x-8)

Solution for Y=6(2x+3)(3x-8) equation:

=6(2Y+3)(3Y-8)

We move all terms to the left:

-(6(2Y+3)(3Y-8))=0

We multiply parentheses ..

-(6(+6Y^2-16Y+9Y-24))=0


We calculate terms in parentheses: -(6(+6Y^2-16Y+9Y-24)), so:

6(+6Y^2-16Y+9Y-24)

We multiply parentheses

36Y^2-96Y+54Y-144

We add all the numbers together, and all the variables

36Y^2-42Y-144

Back to the equation:

-(36Y^2-42Y-144)


We get rid of parentheses

-36Y^2+42Y+144=0

a = -36; b = 42; c = +144;
Δ = b2-4ac
Δ = 422-4·(-36)·144
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-150}{2*-36}=\frac{-192}{-72}
=2+2/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+150}{2*-36}=\frac{108}{-72}
=-1+1/2
$