-16x^2+31x+2=0

Solution for -16x^2+31x+2=0 equation:

-16x^2+31x+2=0

a = -16; b = 31; c = +2;
Δ = b2-4ac
Δ = 312-4·(-16)·2
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-33}{2*-16}=\frac{-64}{-32}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+33}{2*-16}=\frac{2}{-32}
=-1/16
$