12665=x^2+15x+65

Solution for 12665=x^2+15x+65 equation:

12665=x^2+15x+65

We move all terms to the left:

12665-(x^2+15x+65)=0

We get rid of parentheses

-x^2-15x-65+12665=0

We add all the numbers together, and all the variables

-1x^2-15x+12600=0

a = -1; b = -15; c = +12600;
Δ = b2-4ac
Δ = -152-4·(-1)·12600
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-225}{2*-1}=\frac{-210}{-2}
=+105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+225}{2*-1}=\frac{240}{-2}
=-120
$