x^2-7x-1=16

Solution for x^2-7x-1=16 equation:

x^2-7x-1=16

We move all terms to the left:

x^2-7x-1-(16)=0

We add all the numbers together, and all the variables

x^2-7x-17=0

a = 1; b = -7; c = -17;
Δ = b2-4ac
Δ = -72-4·1·(-17)
Δ = 117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{13}}{2*1}=\frac{7-3\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{13}}{2*1}=\frac{7+3\sqrt{13}}{2}
$