-5t^2-17t-1=0

Solution for -5t^2-17t-1=0 equation:

-5t^2-17t-1=0

a = -5; b = -17; c = -1;
Δ = b2-4ac
Δ = -172-4·(-5)·(-1)
Δ = 269
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{-(-17)-\sqrt{269}}{2*-5}=\frac{17-\sqrt{269}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{269}}{2*-5}=\frac{17+\sqrt{269}}{-10}
$