x^2-16x=13

Solution for x^2-16x=13 equation:

x^2-16x=13

We move all terms to the left:

x^2-16x-(13)=0

a = 1; b = -16; c = -13;
Δ = b2-4ac
Δ = -162-4·1·(-13)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{77}}{2*1}=\frac{16-2\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{77}}{2*1}=\frac{16+2\sqrt{77}}{2}
$