3x^2-8x-254=0

Solution for 3x^2-8x-254=0 equation:

3x^2-8x-254=0

a = 3; b = -8; c = -254;
Δ = b2-4ac
Δ = -82-4·3·(-254)
Δ = 3112
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:

$\sqrt{\Delta}=\sqrt{3112}=\sqrt{4*778}=\sqrt{4}*\sqrt{778}=2\sqrt{778}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{778}}{2*3}=\frac{8-2\sqrt{778}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{778}}{2*3}=\frac{8+2\sqrt{778}}{6}
$