6t^2+100t-12500=0

Solution for 6t^2+100t-12500=0 equation:

6t^2+100t-12500=0

a = 6; b = 100; c = -12500;
Δ = b2-4ac
Δ = 1002-4·6·(-12500)
Δ = 310000
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:

$\sqrt{\Delta}=\sqrt{310000}=\sqrt{10000*31}=\sqrt{10000}*\sqrt{31}=100\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{31}}{2*6}=\frac{-100-100\sqrt{31}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{31}}{2*6}=\frac{-100+100\sqrt{31}}{12}
$