5x^2-2x-165=0

Solution for 5x^2-2x-165=0 equation:

5x^2-2x-165=0

a = 5; b = -2; c = -165;
Δ = b2-4ac
Δ = -22-4·5·(-165)
Δ = 3304
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:

$\sqrt{\Delta}=\sqrt{3304}=\sqrt{4*826}=\sqrt{4}*\sqrt{826}=2\sqrt{826}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{826}}{2*5}=\frac{2-2\sqrt{826}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{826}}{2*5}=\frac{2+2\sqrt{826}}{10}
$