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

Solution for (x-2)(1.5-3x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+7.5x-3=0

a = -3; b = 7.5; c = -3;
Δ = b2-4ac
Δ = 7.52-4·(-3)·(-3)
Δ = 20.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7.5)-\sqrt{20.25}}{2*-3}=\frac{-7.5-\sqrt{20.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{20.25}}{2*-3}=\frac{-7.5+\sqrt{20.25}}{-6}
$