-16x^2+31x+5=19

Solution for -16x^2+31x+5=19 equation:

-16x^2+31x+5=19

We move all terms to the left:

-16x^2+31x+5-(19)=0

We add all the numbers together, and all the variables

-16x^2+31x-14=0

a = -16; b = 31; c = -14;
Δ = b2-4ac
Δ = 312-4·(-16)·(-14)
Δ = 65
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{65}}{2*-16}=\frac{-31-\sqrt{65}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{65}}{2*-16}=\frac{-31+\sqrt{65}}{-32}
$