-x2+13x=1

Solution for -x2+13x=1 equation:

-x2+13x=1

We move all terms to the left:

-x2+13x-(1)=0

We add all the numbers together, and all the variables

-1x^2+13x-1=0

a = -1; b = 13; c = -1;
Δ = b2-4ac
Δ = 132-4·(-1)·(-1)
Δ = 165
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{-(13)-\sqrt{165}}{2*-1}=\frac{-13-\sqrt{165}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{165}}{2*-1}=\frac{-13+\sqrt{165}}{-2}
$