1.5x^2-9x+9.5=0

Solution for 1.5x^2-9x+9.5=0 equation:

1.5x^2-9x+9.5=0

a = 1.5; b = -9; c = +9.5;
Δ = b2-4ac
Δ = -92-4·1.5·9.5
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-2\sqrt{6}}{2*1.5}=\frac{9-2\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+2\sqrt{6}}{2*1.5}=\frac{9+2\sqrt{6}}{3}
$