5t^2-2t-250=0

Solution for 5t^2-2t-250=0 equation:

5t^2-2t-250=0

a = 5; b = -2; c = -250;
Δ = b2-4ac
Δ = -22-4·5·(-250)
Δ = 5004
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:

$\sqrt{\Delta}=\sqrt{5004}=\sqrt{36*139}=\sqrt{36}*\sqrt{139}=6\sqrt{139}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{139}}{2*5}=\frac{2-6\sqrt{139}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{139}}{2*5}=\frac{2+6\sqrt{139}}{10}
$