x^2+x-65=0

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

x^2+x-65=0

a = 1; b = 1; c = -65;
Δ = b2-4ac
Δ = 12-4·1·(-65)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{29}}{2*1}=\frac{-1-3\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{29}}{2*1}=\frac{-1+3\sqrt{29}}{2}
$