Y=(4x-6)(8x+4)

Solution for Y=(4x-6)(8x+4) equation:

=(4Y-6)(8Y+4)

We move all terms to the left:

-((4Y-6)(8Y+4))=0

We multiply parentheses ..

-((+32Y^2+16Y-48Y-24))=0


We calculate terms in parentheses: -((+32Y^2+16Y-48Y-24)), so:

(+32Y^2+16Y-48Y-24)

We get rid of parentheses

32Y^2+16Y-48Y-24

We add all the numbers together, and all the variables

32Y^2-32Y-24

Back to the equation:

-(32Y^2-32Y-24)


We get rid of parentheses

-32Y^2+32Y+24=0

a = -32; b = 32; c = +24;
Δ = b2-4ac
Δ = 322-4·(-32)·24
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-64}{2*-32}=\frac{-96}{-64}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+64}{2*-32}=\frac{32}{-64}
=-1/2
$