0=-16x^2+5x+6

Solution for 0=-16x^2+5x+6 equation:

0=-16x^2+5x+6

We move all terms to the left:

0-(-16x^2+5x+6)=0

We add all the numbers together, and all the variables

-(-16x^2+5x+6)=0

We get rid of parentheses

16x^2-5x-6=0

a = 16; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·16·(-6)
Δ = 409
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{-(-5)-\sqrt{409}}{2*16}=\frac{5-\sqrt{409}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{409}}{2*16}=\frac{5+\sqrt{409}}{32}
$