32=1.5x^2+2x

Solution for 32=1.5x^2+2x equation:

32=1.5x^2+2x

We move all terms to the left:

32-(1.5x^2+2x)=0

We get rid of parentheses

-1.5x^2-2x+32=0

a = -1.5; b = -2; c = +32;
Δ = b2-4ac
Δ = -22-4·(-1.5)·32
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*-1.5}=\frac{-12}{-3}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*-1.5}=\frac{16}{-3}
=-5+1/3
$