16t^2-200=31

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

16t^2-200=31

We move all terms to the left:

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

We add all the numbers together, and all the variables

16t^2-231=0

a = 16; b = 0; c = -231;
Δ = b2-4ac
Δ = 02-4·16·(-231)
Δ = 14784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14784}=\sqrt{64*231}=\sqrt{64}*\sqrt{231}=8\sqrt{231}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{231}}{2*16}=\frac{0-8\sqrt{231}}{32}
=-\frac{8\sqrt{231}}{32}
=-\frac{\sqrt{231}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{231}}{2*16}=\frac{0+8\sqrt{231}}{32}
=\frac{8\sqrt{231}}{32}
=\frac{\sqrt{231}}{4}
$