9=3x(5x-2)

Solution for 9=3x(5x-2) equation:

9=3x(5x-2)

We move all terms to the left:

9-(3x(5x-2))=0


We calculate terms in parentheses: -(3x(5x-2)), so:

3x(5x-2)

We multiply parentheses

15x^2-6x

Back to the equation:

-(15x^2-6x)


We get rid of parentheses

-15x^2+6x+9=0

a = -15; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-15)·9
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*-15}=\frac{-30}{-30}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*-15}=\frac{18}{-30}
=-3/5
$