16t^2-72t=464

Solution for 16t^2-72t=464 equation:

16t^2-72t=464

We move all terms to the left:

16t^2-72t-(464)=0

a = 16; b = -72; c = -464;
Δ = b2-4ac
Δ = -722-4·16·(-464)
Δ = 34880
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:

$\sqrt{\Delta}=\sqrt{34880}=\sqrt{64*545}=\sqrt{64}*\sqrt{545}=8\sqrt{545}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{545}}{2*16}=\frac{72-8\sqrt{545}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{545}}{2*16}=\frac{72+8\sqrt{545}}{32}
$