156t-16t^2=21

Solution for 156t-16t^2=21 equation:

156t-16t^2=21

We move all terms to the left:

156t-16t^2-(21)=0

a = -16; b = 156; c = -21;
Δ = b2-4ac
Δ = 1562-4·(-16)·(-21)
Δ = 22992
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:

$\sqrt{\Delta}=\sqrt{22992}=\sqrt{16*1437}=\sqrt{16}*\sqrt{1437}=4\sqrt{1437}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-4\sqrt{1437}}{2*-16}=\frac{-156-4\sqrt{1437}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+4\sqrt{1437}}{2*-16}=\frac{-156+4\sqrt{1437}}{-32}
$