1.5*x^2+5*x+1.5=0

Solution for 1.5*x^2+5*x+1.5=0 equation:

1.5x^2+5x+1.5=0

a = 1.5; b = 5; c = +1.5;
Δ = b2-4ac
Δ = 52-4·1.5·1.5
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{-(5)-4}{2*1.5}=\frac{-9}{3}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+4}{2*1.5}=\frac{-1}{3}
=-1/3
$