3t^2+60t-6000=0

Solution for 3t^2+60t-6000=0 equation:

3t^2+60t-6000=0

a = 3; b = 60; c = -6000;
Δ = b2-4ac
Δ = 602-4·3·(-6000)
Δ = 75600
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:

$\sqrt{\Delta}=\sqrt{75600}=\sqrt{3600*21}=\sqrt{3600}*\sqrt{21}=60\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60\sqrt{21}}{2*3}=\frac{-60-60\sqrt{21}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60\sqrt{21}}{2*3}=\frac{-60+60\sqrt{21}}{6}
$