31=200-16x^2

Solution for 31=200-16x^2 equation:

31=200-16x^2

We move all terms to the left:

31-(200-16x^2)=0

We get rid of parentheses

16x^2-200+31=0

We add all the numbers together, and all the variables

16x^2-169=0

a = 16; b = 0; c = -169;
Δ = b2-4ac
Δ = 02-4·16·(-169)
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104}{2*16}=\frac{-104}{32}
=-3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104}{2*16}=\frac{104}{32}
=3+1/4
$