3000t^2+4000t-50000=0

Solution for 3000t^2+4000t-50000=0 equation:

3000t^2+4000t-50000=0

a = 3000; b = 4000; c = -50000;
Δ = b2-4ac
Δ = 40002-4·3000·(-50000)
Δ = 616000000
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:

$\sqrt{\Delta}=\sqrt{616000000}=\sqrt{4000000*154}=\sqrt{4000000}*\sqrt{154}=2000\sqrt{154}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4000)-2000\sqrt{154}}{2*3000}=\frac{-4000-2000\sqrt{154}}{6000}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4000)+2000\sqrt{154}}{2*3000}=\frac{-4000+2000\sqrt{154}}{6000}
$