16t^2-484=533

Solution for 16t^2-484=533 equation:

16t^2-484=533

We move all terms to the left:

16t^2-484-(533)=0

We add all the numbers together, and all the variables

16t^2-1017=0

a = 16; b = 0; c = -1017;
Δ = b2-4ac
Δ = 02-4·16·(-1017)
Δ = 65088
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:

$\sqrt{\Delta}=\sqrt{65088}=\sqrt{576*113}=\sqrt{576}*\sqrt{113}=24\sqrt{113}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{113}}{2*16}=\frac{0-24\sqrt{113}}{32}
=-\frac{24\sqrt{113}}{32}
=-\frac{3\sqrt{113}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{113}}{2*16}=\frac{0+24\sqrt{113}}{32}
=\frac{24\sqrt{113}}{32}
=\frac{3\sqrt{113}}{4}
$