-1,5q^2-6q+12,5=0

Solution for -1,5q^2-6q+12,5=0 equation:

-1.5q^2-6q+12.5=0

a = -1.5; b = -6; c = +12.5;
Δ = b2-4ac
Δ = -62-4·(-1.5)·12.5
Δ = 111
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{-(-6)-\sqrt{111}}{2*-1.5}=\frac{6-\sqrt{111}}{-3}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{111}}{2*-1.5}=\frac{6+\sqrt{111}}{-3}
$