x(-2x+-13)=1

Solution for x(-2x+-13)=1 equation:

x(-2x+-13)=1

We move all terms to the left:

x(-2x+-13)-(1)=0

We add all the numbers together, and all the variables

x(-2x-13)-1=0

We multiply parentheses

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

a = -2; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·(-2)·(-1)
Δ = 161
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{161}}{2*-2}=\frac{13-\sqrt{161}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{161}}{2*-2}=\frac{13+\sqrt{161}}{-4}
$