Y=4(2y-1)(-7+2y)

Solution for Y=4(2y-1)(-7+2y) equation:

=4(2Y-1)(-7+2Y)

We move all terms to the left:

-(4(2Y-1)(-7+2Y))=0

We add all the numbers together, and all the variables

-(4(2Y-1)(2Y-7))=0

We multiply parentheses ..

-(4(+4Y^2-14Y-2Y+7))=0


We calculate terms in parentheses: -(4(+4Y^2-14Y-2Y+7)), so:

4(+4Y^2-14Y-2Y+7)

We multiply parentheses

16Y^2-56Y-8Y+28

We add all the numbers together, and all the variables

16Y^2-64Y+28

Back to the equation:

-(16Y^2-64Y+28)


We get rid of parentheses

-16Y^2+64Y-28=0

a = -16; b = 64; c = -28;
Δ = b2-4ac
Δ = 642-4·(-16)·(-28)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-48}{2*-16}=\frac{-112}{-32}
=3+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+48}{2*-16}=\frac{-16}{-32}
=1/2
$