16t^2+216t=97

Solution for 16t^2+216t=97 equation:

16t^2+216t=97

We move all terms to the left:

16t^2+216t-(97)=0

a = 16; b = 216; c = -97;
Δ = b2-4ac
Δ = 2162-4·16·(-97)
Δ = 52864
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:

$\sqrt{\Delta}=\sqrt{52864}=\sqrt{64*826}=\sqrt{64}*\sqrt{826}=8\sqrt{826}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-8\sqrt{826}}{2*16}=\frac{-216-8\sqrt{826}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+8\sqrt{826}}{2*16}=\frac{-216+8\sqrt{826}}{32}
$