-4n(1-2n)=4n+4(n+5)

Solution for -4n(1-2n)=4n+4(n+5) equation:

-4n(1-2n)=4n+4(n+5)

We move all terms to the left:

-4n(1-2n)-(4n+4(n+5))=0

We add all the numbers together, and all the variables

-4n(-2n+1)-(4n+4(n+5))=0

We multiply parentheses

8n^2-4n-(4n+4(n+5))=0


We calculate terms in parentheses: -(4n+4(n+5)), so:

4n+4(n+5)

We multiply parentheses

4n+4n+20

We add all the numbers together, and all the variables

8n+20

Back to the equation:

-(8n+20)


We get rid of parentheses

8n^2-4n-8n-20=0

We add all the numbers together, and all the variables

8n^2-12n-20=0

a = 8; b = -12; c = -20;
Δ = b2-4ac
Δ = -122-4·8·(-20)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28}{2*8}=\frac{-16}{16}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28}{2*8}=\frac{40}{16}
=2+1/2
$