0=3x^2+x-16

Solution for 0=3x^2+x-16 equation:

0=3x^2+x-16

We move all terms to the left:

0-(3x^2+x-16)=0

We add all the numbers together, and all the variables

-(3x^2+x-16)=0

We get rid of parentheses

-3x^2-x+16=0

We add all the numbers together, and all the variables

-3x^2-1x+16=0

a = -3; b = -1; c = +16;
Δ = b2-4ac
Δ = -12-4·(-3)·16
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{-(-1)-\sqrt{193}}{2*-3}=\frac{1-\sqrt{193}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{193}}{2*-3}=\frac{1+\sqrt{193}}{-6}
$