1.50t^2-30.0t-30.0=0

Solution for 1.50t^2-30.0t-30.0=0 equation:

1.50t^2-30.0t-30.0=0

We add all the numbers together, and all the variables

1.50t^2-30t-30=0

a = 1.50; b = -30; c = -30;
Δ = b2-4ac
Δ = -302-4·1.50·(-30)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{30}}{2*1.50}=\frac{30-6\sqrt{30}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{30}}{2*1.50}=\frac{30+6\sqrt{30}}{3}
$