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

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

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

We move all terms to the left:

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


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

3(x-2)x

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+11x-9=0

a = -3; b = 11; c = -9;
Δ = b2-4ac
Δ = 112-4·(-3)·(-9)
Δ = 13
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{-(11)-\sqrt{13}}{2*-3}=\frac{-11-\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{13}}{2*-3}=\frac{-11+\sqrt{13}}{-6}
$