9=1.5q^2+4q

Solution for 9=1.5q^2+4q equation:

9=1.5q^2+4q

We move all terms to the left:

9-(1.5q^2+4q)=0

We get rid of parentheses

-1.5q^2-4q+9=0

a = -1.5; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-1.5)·9
Δ = 70
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{70}}{2*-1.5}=\frac{4-\sqrt{70}}{-3}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{70}}{2*-1.5}=\frac{4+\sqrt{70}}{-3}
$