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

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

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

We move all terms to the left:

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


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

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+9x+6x-5=0

We add all the numbers together, and all the variables

-3x^2+15x-5=0

a = -3; b = 15; c = -5;
Δ = b2-4ac
Δ = 152-4·(-3)·(-5)
Δ = 165
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{-(15)-\sqrt{165}}{2*-3}=\frac{-15-\sqrt{165}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{165}}{2*-3}=\frac{-15+\sqrt{165}}{-6}
$