-31-29n=-5n+5-5n^2

Solution for -31-29n=-5n+5-5n^2 equation:

-31-29n=-5n+5-5n^2

We move all terms to the left:

-31-29n-(-5n+5-5n^2)=0

We get rid of parentheses

5n^2+5n-29n-5-31=0

We add all the numbers together, and all the variables

5n^2-24n-36=0

a = 5; b = -24; c = -36;
Δ = b2-4ac
Δ = -242-4·5·(-36)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*5}=\frac{-12}{10}
=-1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*5}=\frac{60}{10}
=6
$