1.5x^2+4.5x=3

Solution for 1.5x^2+4.5x=3 equation:

1.5x^2+4.5x=3

We move all terms to the left:

1.5x^2+4.5x-(3)=0

a = 1.5; b = 4.5; c = -3;
Δ = b2-4ac
Δ = 4.52-4·1.5·(-3)
Δ = 38.25
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{-(4.5)-\sqrt{38.25}}{2*1.5}=\frac{-4.5-\sqrt{38.25}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{38.25}}{2*1.5}=\frac{-4.5+\sqrt{38.25}}{3}
$