150-6t-4.9t^2=0

Solution for 150-6t-4.9t^2=0 equation:

150-6t-4.9t^2=0

a = -4.9; b = -6; c = +150;
Δ = b2-4ac
Δ = -62-4·(-4.9)·150
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{186}}{2*-4.9}=\frac{6-4\sqrt{186}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{186}}{2*-4.9}=\frac{6+4\sqrt{186}}{-9.8}
$