3x+1.5x^2=72

Solution for 3x+1.5x^2=72 equation:

3x+1.5x^2=72

We move all terms to the left:

3x+1.5x^2-(72)=0

a = 1.5; b = 3; c = -72;
Δ = b2-4ac
Δ = 32-4·1.5·(-72)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*1.5}=\frac{-24}{3}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*1.5}=\frac{18}{3}
=6
$