-15(n+1)=-4n(n+11)

Solution for -15(n+1)=-4n(n+11) equation:

-15(n+1)=-4n(n+11)

We move all terms to the left:

-15(n+1)-(-4n(n+11))=0

We multiply parentheses

-15n-(-4n(n+11))-15=0


We calculate terms in parentheses: -(-4n(n+11)), so:

-4n(n+11)

We multiply parentheses

-4n^2-44n

Back to the equation:

-(-4n^2-44n)


We get rid of parentheses

4n^2+44n-15n-15=0

We add all the numbers together, and all the variables

4n^2+29n-15=0

a = 4; b = 29; c = -15;
Δ = b2-4ac
Δ = 292-4·4·(-15)
Δ = 1081
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{-(29)-\sqrt{1081}}{2*4}=\frac{-29-\sqrt{1081}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1081}}{2*4}=\frac{-29+\sqrt{1081}}{8}
$