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

Solution for 2(4-a)=4a(2a-8) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2(-1a+4)-(4a(2a-8))=0

We multiply parentheses

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


We calculate terms in parentheses: -(4a(2a-8)), so:

4a(2a-8)

We multiply parentheses

8a^2-32a

Back to the equation:

-(8a^2-32a)


We get rid of parentheses

-8a^2-2a+32a+8=0

We add all the numbers together, and all the variables

-8a^2+30a+8=0

a = -8; b = 30; c = +8;
Δ = b2-4ac
Δ = 302-4·(-8)·8
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-34}{2*-8}=\frac{-64}{-16}
=+4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+34}{2*-8}=\frac{4}{-16}
=-1/4
$