x(6-3x/2)=1.5

Solution for x(6-3x/2)=1.5 equation:

x(6-3x/2)=1.5

We move all terms to the left:

x(6-3x/2)-(1.5)=0

We add all the numbers together, and all the variables

x(-3x/2+6)-(1.5)=0

We add all the numbers together, and all the variables

x(-3x/2+6)-1.5=0

We multiply parentheses

-3x^2+6x-1.5=0

a = -3; b = 6; c = -1.5;
Δ = b2-4ac
Δ = 62-4·(-3)·(-1.5)
Δ = 18
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:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-3\sqrt{2}}{2*-3}=\frac{-6-3\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+3\sqrt{2}}{2*-3}=\frac{-6+3\sqrt{2}}{-6}
$