x^2-6x-69=0

Solution for x^2-6x-69=0 equation:

x^2-6x-69=0

a = 1; b = -6; c = -69;
Δ = b2-4ac
Δ = -62-4·1·(-69)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{78}}{2*1}=\frac{6-2\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{78}}{2*1}=\frac{6+2\sqrt{78}}{2}
$