3x2-40x-117=0

Solution for 3x2-40x-117=0 equation:

3x^2-40x-117=0

a = 3; b = -40; c = -117;
Δ = b2-4ac
Δ = -402-4·3·(-117)
Δ = 3004
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:

$\sqrt{\Delta}=\sqrt{3004}=\sqrt{4*751}=\sqrt{4}*\sqrt{751}=2\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{751}}{2*3}=\frac{40-2\sqrt{751}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{751}}{2*3}=\frac{40+2\sqrt{751}}{6}
$