0=-16x^2+44x+5

Solution for 0=-16x^2+44x+5 equation:

0=-16x^2+44x+5

We move all terms to the left:

0-(-16x^2+44x+5)=0

We add all the numbers together, and all the variables

-(-16x^2+44x+5)=0

We get rid of parentheses

16x^2-44x-5=0

a = 16; b = -44; c = -5;
Δ = b2-4ac
Δ = -442-4·16·(-5)
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{141}}{2*16}=\frac{44-4\sqrt{141}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{141}}{2*16}=\frac{44+4\sqrt{141}}{32}
$