1,5x^2+3x=120

Solution for 1,5x^2+3x=120 equation:

1.5x^2+3x=120

We move all terms to the left:

1.5x^2+3x-(120)=0

a = 1.5; b = 3; c = -120;
Δ = b2-4ac
Δ = 32-4·1.5·(-120)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*1.5}=\frac{-30}{3}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*1.5}=\frac{24}{3}
=8
$