2x2-13x=1

Solution for 2x2-13x=1 equation:

2x^2-13x=1

We move all terms to the left:

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

a = 2; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·2·(-1)
Δ = 177
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{177}}{2*2}=\frac{13-\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{177}}{2*2}=\frac{13+\sqrt{177}}{4}
$