x(x-15)=1

Solution for x(x-15)=1 equation:

x(x-15)=1

We move all terms to the left:

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

We multiply parentheses

x^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}
$