2t2-50t-50000=0

Solution for 2t2-50t-50000=0 equation:

2t^2-50t-50000=0

a = 2; b = -50; c = -50000;
Δ = b2-4ac
Δ = -502-4·2·(-50000)
Δ = 402500
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:

$\sqrt{\Delta}=\sqrt{402500}=\sqrt{2500*161}=\sqrt{2500}*\sqrt{161}=50\sqrt{161}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{161}}{2*2}=\frac{50-50\sqrt{161}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{161}}{2*2}=\frac{50+50\sqrt{161}}{4}
$