3x^2-8x-1600=0

Solution for 3x^2-8x-1600=0 equation:

3x^2-8x-1600=0

a = 3; b = -8; c = -1600;
Δ = b2-4ac
Δ = -82-4·3·(-1600)
Δ = 19264
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:

$\sqrt{\Delta}=\sqrt{19264}=\sqrt{64*301}=\sqrt{64}*\sqrt{301}=8\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{301}}{2*3}=\frac{8-8\sqrt{301}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{301}}{2*3}=\frac{8+8\sqrt{301}}{6}
$