5x^2-6x-65=0

Solution for 5x^2-6x-65=0 equation:

5x^2-6x-65=0

a = 5; b = -6; c = -65;
Δ = b2-4ac
Δ = -62-4·5·(-65)
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{334}}{2*5}=\frac{6-2\sqrt{334}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{334}}{2*5}=\frac{6+2\sqrt{334}}{10}
$