45=x(3x-6)

Solution for 45=x(3x-6) equation:

45=x(3x-6)

We move all terms to the left:

45-(x(3x-6))=0


We calculate terms in parentheses: -(x(3x-6)), so:

x(3x-6)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+6x+45=0

a = -3; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-3)·45
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*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*-3}=\frac{18}{-6}
=-3
$