0=x^2-2x-465

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

0=x^2-2x-465

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+2x+465=0

We add all the numbers together, and all the variables

-1x^2+2x+465=0

a = -1; b = 2; c = +465;
Δ = b2-4ac
Δ = 22-4·(-1)·465
Δ = 1864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1864}=\sqrt{4*466}=\sqrt{4}*\sqrt{466}=2\sqrt{466}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{466}}{2*-1}=\frac{-2-2\sqrt{466}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{466}}{2*-1}=\frac{-2+2\sqrt{466}}{-2}
$