12x^2-36x+1.5=0

Solution for 12x^2-36x+1.5=0 equation:

12x^2-36x+1.5=0

a = 12; b = -36; c = +1.5;
Δ = b2-4ac
Δ = -362-4·12·1.5
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{34}}{2*12}=\frac{36-6\sqrt{34}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{34}}{2*12}=\frac{36+6\sqrt{34}}{24}
$