4.5t^2+3t-2=0

Solution for 4.5t^2+3t-2=0 equation:

4.5t^2+3t-2=0

a = 4.5; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·4.5·(-2)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{5}}{2*4.5}=\frac{-3-3\sqrt{5}}{9}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{5}}{2*4.5}=\frac{-3+3\sqrt{5}}{9}
$