-3x2-31x-64=0

Solution for -3x2-31x-64=0 equation:

-3x^2-31x-64=0

a = -3; b = -31; c = -64;
Δ = b2-4ac
Δ = -312-4·(-3)·(-64)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{193}}{2*-3}=\frac{31-\sqrt{193}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{193}}{2*-3}=\frac{31+\sqrt{193}}{-6}
$