-4y(24+8y)=-64

Solution for -4y(24+8y)=-64 equation:

-4y(24+8y)=-64

We move all terms to the left:

-4y(24+8y)-(-64)=0

We add all the numbers together, and all the variables

-4y(8y+24)-(-64)=0

We add all the numbers together, and all the variables

-4y(8y+24)+64=0

We multiply parentheses

-32y^2-96y+64=0

a = -32; b = -96; c = +64;
Δ = b2-4ac
Δ = -962-4·(-32)·64
Δ = 17408
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17408}=\sqrt{1024*17}=\sqrt{1024}*\sqrt{17}=32\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-32\sqrt{17}}{2*-32}=\frac{96-32\sqrt{17}}{-64}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+32\sqrt{17}}{2*-32}=\frac{96+32\sqrt{17}}{-64}
$