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

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

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

We move all terms to the left:

2(a-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+34a-8=0

a = -8; b = 34; c = -8;
Δ = b2-4ac
Δ = 342-4·(-8)·(-8)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-30}{2*-8}=\frac{-64}{-16}
=+4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+30}{2*-8}=\frac{-4}{-16}
=1/4
$