16t^2-12t-975=0

Solution for 16t^2-12t-975=0 equation:

16t^2-12t-975=0

a = 16; b = -12; c = -975;
Δ = b2-4ac
Δ = -122-4·16·(-975)
Δ = 62544
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:

$\sqrt{\Delta}=\sqrt{62544}=\sqrt{16*3909}=\sqrt{16}*\sqrt{3909}=4\sqrt{3909}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3909}}{2*16}=\frac{12-4\sqrt{3909}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3909}}{2*16}=\frac{12+4\sqrt{3909}}{32}
$