0=16x^2+100x+85

Solution for 0=16x^2+100x+85 equation:

0=16x^2+100x+85

We move all terms to the left:

0-(16x^2+100x+85)=0

We add all the numbers together, and all the variables

-(16x^2+100x+85)=0

We get rid of parentheses

-16x^2-100x-85=0

a = -16; b = -100; c = -85;
Δ = b2-4ac
Δ = -1002-4·(-16)·(-85)
Δ = 4560
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:

$\sqrt{\Delta}=\sqrt{4560}=\sqrt{16*285}=\sqrt{16}*\sqrt{285}=4\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{285}}{2*-16}=\frac{100-4\sqrt{285}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{285}}{2*-16}=\frac{100+4\sqrt{285}}{-32}
$