-2.7t^2+30t-7.5=0

Solution for -2.7t^2+30t-7.5=0 equation:

-2.7t^2+30t-7.5=0

a = -2.7; b = 30; c = -7.5;
Δ = b2-4ac
Δ = 302-4·(-2.7)·(-7.5)
Δ = 819
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:

$\sqrt{\Delta}=\sqrt{819}=\sqrt{9*91}=\sqrt{9}*\sqrt{91}=3\sqrt{91}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-3\sqrt{91}}{2*-2.7}=\frac{-30-3\sqrt{91}}{-5.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+3\sqrt{91}}{2*-2.7}=\frac{-30+3\sqrt{91}}{-5.4}
$