0=16x^2+100x+5

Solution for 0=16x^2+100x+5 equation:

0=16x^2+100x+5

We move all terms to the left:

0-(16x^2+100x+5)=0

We add all the numbers together, and all the variables

-(16x^2+100x+5)=0

We get rid of parentheses

-16x^2-100x-5=0

a = -16; b = -100; c = -5;
Δ = b2-4ac
Δ = -1002-4·(-16)·(-5)
Δ = 9680
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:

$\sqrt{\Delta}=\sqrt{9680}=\sqrt{1936*5}=\sqrt{1936}*\sqrt{5}=44\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-44\sqrt{5}}{2*-16}=\frac{100-44\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+44\sqrt{5}}{2*-16}=\frac{100+44\sqrt{5}}{-32}
$