-3x^2+9x+2.25=0

Solution for -3x^2+9x+2.25=0 equation:

-3x^2+9x+2.25=0

a = -3; b = 9; c = +2.25;
Δ = b2-4ac
Δ = 92-4·(-3)·2.25
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-6\sqrt{3}}{2*-3}=\frac{-9-6\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+6\sqrt{3}}{2*-3}=\frac{-9+6\sqrt{3}}{-6}
$