16t^2+384t+4=1284

Solution for 16t^2+384t+4=1284 equation:

16t^2+384t+4=1284

We move all terms to the left:

16t^2+384t+4-(1284)=0

We add all the numbers together, and all the variables

16t^2+384t-1280=0

a = 16; b = 384; c = -1280;
Δ = b2-4ac
Δ = 3842-4·16·(-1280)
Δ = 229376
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:

$\sqrt{\Delta}=\sqrt{229376}=\sqrt{16384*14}=\sqrt{16384}*\sqrt{14}=128\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-128\sqrt{14}}{2*16}=\frac{-384-128\sqrt{14}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+128\sqrt{14}}{2*16}=\frac{-384+128\sqrt{14}}{32}
$