4(a-5)=8a(4a-20)

Solution for 4(a-5)=8a(4a-20) equation:

4(a-5)=8a(4a-20)

We move all terms to the left:

4(a-5)-(8a(4a-20))=0

We multiply parentheses

4a-(8a(4a-20))-20=0


We calculate terms in parentheses: -(8a(4a-20)), so:

8a(4a-20)

We multiply parentheses

32a^2-160a

Back to the equation:

-(32a^2-160a)


We get rid of parentheses

-32a^2+4a+160a-20=0

We add all the numbers together, and all the variables

-32a^2+164a-20=0

a = -32; b = 164; c = -20;
Δ = b2-4ac
Δ = 1642-4·(-32)·(-20)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(164)-156}{2*-32}=\frac{-320}{-64}
=+5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(164)+156}{2*-32}=\frac{-8}{-64}
=1/8
$