13265=x^2+10x+65

Solution for 13265=x^2+10x+65 equation:

13265=x^2+10x+65

We move all terms to the left:

13265-(x^2+10x+65)=0

We get rid of parentheses

-x^2-10x-65+13265=0

We add all the numbers together, and all the variables

-1x^2-10x+13200=0

a = -1; b = -10; c = +13200;
Δ = b2-4ac
Δ = -102-4·(-1)·13200
Δ = 52900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{52900}=230$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-230}{2*-1}=\frac{-220}{-2}
=+110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+230}{2*-1}=\frac{240}{-2}
=-120
$