x^2-13x=5

Solution for x^2-13x=5 equation:

x^2-13x=5

We move all terms to the left:

x^2-13x-(5)=0

a = 1; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·1·(-5)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{21}}{2*1}=\frac{13-3\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{21}}{2*1}=\frac{13+3\sqrt{21}}{2}
$