0=x^2-15x-1

Solution for 0=x^2-15x-1 equation:

0=x^2-15x-1

We move all terms to the left:

0-(x^2-15x-1)=0

We add all the numbers together, and all the variables

-(x^2-15x-1)=0

We get rid of parentheses

-x^2+15x+1=0

We add all the numbers together, and all the variables

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

a = -1; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-1)·1
Δ = 229
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{-(15)-\sqrt{229}}{2*-1}=\frac{-15-\sqrt{229}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{229}}{2*-1}=\frac{-15+\sqrt{229}}{-2}
$