0=-16x^2+121x+83

Solution for 0=-16x^2+121x+83 equation:

0=-16x^2+121x+83

We move all terms to the left:

0-(-16x^2+121x+83)=0

We add all the numbers together, and all the variables

-(-16x^2+121x+83)=0

We get rid of parentheses

16x^2-121x-83=0

a = 16; b = -121; c = -83;
Δ = b2-4ac
Δ = -1212-4·16·(-83)
Δ = 19953
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:

$\sqrt{\Delta}=\sqrt{19953}=\sqrt{9*2217}=\sqrt{9}*\sqrt{2217}=3\sqrt{2217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-121)-3\sqrt{2217}}{2*16}=\frac{121-3\sqrt{2217}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-121)+3\sqrt{2217}}{2*16}=\frac{121+3\sqrt{2217}}{32}
$