3x^2-8x-500=0

Solution for 3x^2-8x-500=0 equation:

3x^2-8x-500=0

a = 3; b = -8; c = -500;
Δ = b2-4ac
Δ = -82-4·3·(-500)
Δ = 6064
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:

$\sqrt{\Delta}=\sqrt{6064}=\sqrt{16*379}=\sqrt{16}*\sqrt{379}=4\sqrt{379}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{379}}{2*3}=\frac{8-4\sqrt{379}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{379}}{2*3}=\frac{8+4\sqrt{379}}{6}
$