16t(t-4)=117

Solution for 16t(t-4)=117 equation:

16t(t-4)=117

We move all terms to the left:

16t(t-4)-(117)=0

We multiply parentheses

16t^2-64t-117=0

a = 16; b = -64; c = -117;
Δ = b2-4ac
Δ = -642-4·16·(-117)
Δ = 11584
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:

$\sqrt{\Delta}=\sqrt{11584}=\sqrt{64*181}=\sqrt{64}*\sqrt{181}=8\sqrt{181}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{181}}{2*16}=\frac{64-8\sqrt{181}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{181}}{2*16}=\frac{64+8\sqrt{181}}{32}
$