2.25x^2-9x+3=0

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

2.25x^2-9x+3=0

a = 2.25; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·2.25·3
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{6}}{2*2.25}=\frac{9-3\sqrt{6}}{4.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{6}}{2*2.25}=\frac{9+3\sqrt{6}}{4.5}
$