-.6t^2+18t-67.5=0

Solution for -.6t^2+18t-67.5=0 equation:

-.6t^2+18t-67.5=0

We add all the numbers together, and all the variables

-0.6t^2+18t-67.5=0

a = -0.6; b = 18; c = -67.5;
Δ = b2-4ac
Δ = 182-4·(-0.6)·(-67.5)
Δ = 162
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:

$\sqrt{\Delta}=\sqrt{162}=\sqrt{81*2}=\sqrt{81}*\sqrt{2}=9\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-9\sqrt{2}}{2*-0.6}=\frac{-18-9\sqrt{2}}{-1.2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+9\sqrt{2}}{2*-0.6}=\frac{-18+9\sqrt{2}}{-1.2}
$