50t-4t^2-120=0

Solution for 50t-4t^2-120=0 equation:

50t-4t^2-120=0

a = -4; b = 50; c = -120;
Δ = b2-4ac
Δ = 502-4·(-4)·(-120)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{145}}{2*-4}=\frac{-50-2\sqrt{145}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{145}}{2*-4}=\frac{-50+2\sqrt{145}}{-8}
$