x^2-12x-65=0

Solution for x^2-12x-65=0 equation:

x^2-12x-65=0

a = 1; b = -12; c = -65;
Δ = b2-4ac
Δ = -122-4·1·(-65)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{101}}{2*1}=\frac{12-2\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{101}}{2*1}=\frac{12+2\sqrt{101}}{2}
$