200-16x^2=31

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

200-16x^2=31

We move all terms to the left:

200-16x^2-(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
$