4.5t(t-3)-2.7=15.3

Solution for 4.5t(t-3)-2.7=15.3 equation:

4.5t(t-3)-2.7=15.3

We move all terms to the left:

4.5t(t-3)-2.7-(15.3)=0

We add all the numbers together, and all the variables

4.5t(t-3)-18=0

We multiply parentheses

4t^2-12t-18=0

a = 4; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·4·(-18)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{3}}{2*4}=\frac{12-12\sqrt{3}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{3}}{2*4}=\frac{12+12\sqrt{3}}{8}
$