465=n2-n

Solution for 465=n2-n equation:

465=n2-n

We move all terms to the left:

465-(n2-n)=0

We add all the numbers together, and all the variables

-(+n^2-1n)+465=0

We get rid of parentheses

-n^2+1n+465=0

We add all the numbers together, and all the variables

-1n^2+n+465=0

a = -1; b = 1; c = +465;
Δ = b2-4ac
Δ = 12-4·(-1)·465
Δ = 1861
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{-(1)-\sqrt{1861}}{2*-1}=\frac{-1-\sqrt{1861}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1861}}{2*-1}=\frac{-1+\sqrt{1861}}{-2}
$