120=x(3x+2)

Solution for 120=x(3x+2) equation:

120=x(3x+2)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(3x+2)), so:

x(3x+2)

We multiply parentheses

3x^2+2x

Back to the equation:

-(3x^2+2x)


We get rid of parentheses

-3x^2-2x+120=0

a = -3; b = -2; c = +120;
Δ = b2-4ac
Δ = -22-4·(-3)·120
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*-3}=\frac{40}{-6}
=-6+2/3
$