t^2-625*t-9000=0

Solution for t^2-625*t-9000=0 equation:

t^2-625t-9000=0

a = 1; b = -625; c = -9000;
Δ = b2-4ac
Δ = -6252-4·1·(-9000)
Δ = 426625
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:

$\sqrt{\Delta}=\sqrt{426625}=\sqrt{25*17065}=\sqrt{25}*\sqrt{17065}=5\sqrt{17065}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-625)-5\sqrt{17065}}{2*1}=\frac{625-5\sqrt{17065}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-625)+5\sqrt{17065}}{2*1}=\frac{625+5\sqrt{17065}}{2}
$