0=1.5x^2+4x

Solution for 0=1.5x^2+4x equation:

0=1.5x^2+4x

We move all terms to the left:

0-(1.5x^2+4x)=0

We add all the numbers together, and all the variables

-(1.5x^2+4x)=0

We get rid of parentheses

-1.5x^2-4x=0

a = -1.5; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1.5)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1.5}=\frac{0}{-3}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1.5}=\frac{8}{-3}
=-2+2/3
$