2x^2-6x-2.25=0

Solution for 2x^2-6x-2.25=0 equation:

2x^2-6x-2.25=0

a = 2; b = -6; c = -2.25;
Δ = b2-4ac
Δ = -62-4·2·(-2.25)
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{-(-6)-3\sqrt{6}}{2*2}=\frac{6-3\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+3\sqrt{6}}{2*2}=\frac{6+3\sqrt{6}}{4}
$