16t^2-204t+84=0

Solution for 16t^2-204t+84=0 equation:

16t^2-204t+84=0

a = 16; b = -204; c = +84;
Δ = b2-4ac
Δ = -2042-4·16·84
Δ = 36240
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:

$\sqrt{\Delta}=\sqrt{36240}=\sqrt{16*2265}=\sqrt{16}*\sqrt{2265}=4\sqrt{2265}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-4\sqrt{2265}}{2*16}=\frac{204-4\sqrt{2265}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+4\sqrt{2265}}{2*16}=\frac{204+4\sqrt{2265}}{32}
$