50t2-5t-1=0

Solution for 50t2-5t-1=0 equation:

50t^2-5t-1=0

a = 50; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·50·(-1)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*50}=\frac{-10}{100}
=-1/10
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*50}=\frac{20}{100}
=1/5
$