-16t^2+144t=308

Solution for -16t^2+144t=308 equation:

-16t^2+144t=308

We move all terms to the left:

-16t^2+144t-(308)=0

a = -16; b = 144; c = -308;
Δ = b2-4ac
Δ = 1442-4·(-16)·(-308)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-32}{2*-16}=\frac{-176}{-32}
=5+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+32}{2*-16}=\frac{-112}{-32}
=3+1/2
$