Y=(6+4x)(2x-8)

Solution for Y=(6+4x)(2x-8) equation:

=(6+4Y)(2Y-8)

We move all terms to the left:

-((6+4Y)(2Y-8))=0

We add all the numbers together, and all the variables

-((4Y+6)(2Y-8))=0

We multiply parentheses ..

-((+8Y^2-32Y+12Y-48))=0


We calculate terms in parentheses: -((+8Y^2-32Y+12Y-48)), so:

(+8Y^2-32Y+12Y-48)

We get rid of parentheses

8Y^2-32Y+12Y-48

We add all the numbers together, and all the variables

8Y^2-20Y-48

Back to the equation:

-(8Y^2-20Y-48)


We get rid of parentheses

-8Y^2+20Y+48=0

a = -8; b = 20; c = +48;
Δ = b2-4ac
Δ = 202-4·(-8)·48
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-44}{2*-8}=\frac{-64}{-16}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+44}{2*-8}=\frac{24}{-16}
=-1+1/2
$