-8n-(1-4n)=11n(n-11)

Solution for -8n-(1-4n)=11n(n-11) equation:

-8n-(1-4n)=11n(n-11)

We move all terms to the left:

-8n-(1-4n)-(11n(n-11))=0

We add all the numbers together, and all the variables

-8n-(-4n+1)-(11n(n-11))=0

We get rid of parentheses

-8n+4n-(11n(n-11))-1=0


We calculate terms in parentheses: -(11n(n-11)), so:

11n(n-11)

We multiply parentheses

11n^2-121n

Back to the equation:

-(11n^2-121n)


We add all the numbers together, and all the variables

-4n-(11n^2-121n)-1=0

We get rid of parentheses

-11n^2-4n+121n-1=0

We add all the numbers together, and all the variables

-11n^2+117n-1=0

a = -11; b = 117; c = -1;
Δ = b2-4ac
Δ = 1172-4·(-11)·(-1)
Δ = 13645
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-\sqrt{13645}}{2*-11}=\frac{-117-\sqrt{13645}}{-22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+\sqrt{13645}}{2*-11}=\frac{-117+\sqrt{13645}}{-22}
$