2x^2-13x=-1

Solution for 2x^2-13x=-1 equation:

2x^2-13x=-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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}
$