0=-16x^2+112x+3

Solution for 0=-16x^2+112x+3 equation:

0=-16x^2+112x+3

We move all terms to the left:

0-(-16x^2+112x+3)=0

We add all the numbers together, and all the variables

-(-16x^2+112x+3)=0

We get rid of parentheses

16x^2-112x-3=0

a = 16; b = -112; c = -3;
Δ = b2-4ac
Δ = -1122-4·16·(-3)
Δ = 12736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12736}=\sqrt{64*199}=\sqrt{64}*\sqrt{199}=8\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-8\sqrt{199}}{2*16}=\frac{112-8\sqrt{199}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+8\sqrt{199}}{2*16}=\frac{112+8\sqrt{199}}{32}
$