120=5x+1.5x^2

Solution for 120=5x+1.5x^2 equation:

120=5x+1.5x^2

We move all terms to the left:

120-(5x+1.5x^2)=0

We get rid of parentheses

-1.5x^2-5x+120=0

a = -1.5; b = -5; c = +120;
Δ = b2-4ac
Δ = -52-4·(-1.5)·120
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{745}}{2*-1.5}=\frac{5-\sqrt{745}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{745}}{2*-1.5}=\frac{5+\sqrt{745}}{-3}
$