0=x^2-x-465

Solution for 0=x^2-x-465 equation:

0=x^2-x-465

We move all terms to the left:

0-(x^2-x-465)=0

We add all the numbers together, and all the variables

-(x^2-x-465)=0

We get rid of parentheses

-x^2+x+465=0

We add all the numbers together, and all the variables

-1x^2+x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1861}}{2*-1}=\frac{-1-\sqrt{1861}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1861}}{2*-1}=\frac{-1+\sqrt{1861}}{-2}
$