16t^2-205t-10=0

Solution for 16t^2-205t-10=0 equation:

16t^2-205t-10=0

a = 16; b = -205; c = -10;
Δ = b2-4ac
Δ = -2052-4·16·(-10)
Δ = 42665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-205)-\sqrt{42665}}{2*16}=\frac{205-\sqrt{42665}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-205)+\sqrt{42665}}{2*16}=\frac{205+\sqrt{42665}}{32}
$