1.5t2-45t-45=0

Solution for 1.5t2-45t-45=0 equation:

1.5t^2-45t-45=0

a = 1.5; b = -45; c = -45;
Δ = b2-4ac
Δ = -452-4·1.5·(-45)
Δ = 2295
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:

$\sqrt{\Delta}=\sqrt{2295}=\sqrt{9*255}=\sqrt{9}*\sqrt{255}=3\sqrt{255}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{255}}{2*1.5}=\frac{45-3\sqrt{255}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{255}}{2*1.5}=\frac{45+3\sqrt{255}}{3}
$