120=5x(3x-1)

Solution for 120=5x(3x-1) equation:

120=5x(3x-1)

We move all terms to the left:

120-(5x(3x-1))=0


We calculate terms in parentheses: -(5x(3x-1)), so:

5x(3x-1)

We multiply parentheses

15x^2-5x

Back to the equation:

-(15x^2-5x)


We get rid of parentheses

-15x^2+5x+120=0

a = -15; b = 5; c = +120;
Δ = b2-4ac
Δ = 52-4·(-15)·120
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-85}{2*-15}=\frac{-90}{-30}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+85}{2*-15}=\frac{80}{-30}
=-2+2/3
$