-16t^2=144t=288

Solution for -16t^2=144t=288 equation:

-16t^2=144t=288

We move all terms to the left:

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

a = -16; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-16)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-16}=\frac{0}{-32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-16}=\frac{288}{-32}
=-9
$