61.5t2-50t-10=0

Solution for 61.5t2-50t-10=0 equation:

61.5t^2-50t-10=0

a = 61.5; b = -50; c = -10;
Δ = b2-4ac
Δ = -502-4·61.5·(-10)
Δ = 4960
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:

$\sqrt{\Delta}=\sqrt{4960}=\sqrt{16*310}=\sqrt{16}*\sqrt{310}=4\sqrt{310}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-4\sqrt{310}}{2*61.5}=\frac{50-4\sqrt{310}}{123}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+4\sqrt{310}}{2*61.5}=\frac{50+4\sqrt{310}}{123}
$