2(a-4)=-4a(2a+4)

Solution for 2(a-4)=-4a(2a+4) equation:

2(a-4)=-4a(2a+4)

We move all terms to the left:

2(a-4)-(-4a(2a+4))=0

We multiply parentheses

2a-(-4a(2a+4))-8=0


We calculate terms in parentheses: -(-4a(2a+4)), so:

-4a(2a+4)

We multiply parentheses

-8a^2-16a

Back to the equation:

-(-8a^2-16a)


We get rid of parentheses

8a^2+16a+2a-8=0

We add all the numbers together, and all the variables

8a^2+18a-8=0

a = 8; b = 18; c = -8;
Δ = b2-4ac
Δ = 182-4·8·(-8)
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{145}}{2*8}=\frac{-18-2\sqrt{145}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{145}}{2*8}=\frac{-18+2\sqrt{145}}{16}
$