0=16x^2+177x-5

Solution for 0=16x^2+177x-5 equation:

0=16x^2+177x-5

We move all terms to the left:

0-(16x^2+177x-5)=0

We add all the numbers together, and all the variables

-(16x^2+177x-5)=0

We get rid of parentheses

-16x^2-177x+5=0

a = -16; b = -177; c = +5;
Δ = b2-4ac
Δ = -1772-4·(-16)·5
Δ = 31649
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{-(-177)-\sqrt{31649}}{2*-16}=\frac{177-\sqrt{31649}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+\sqrt{31649}}{2*-16}=\frac{177+\sqrt{31649}}{-32}
$