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

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

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

We move all terms to the left:

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


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

2x(x-3)

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-2)·9
Δ = 193
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{193}}{2*-2}=\frac{-11-\sqrt{193}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{193}}{2*-2}=\frac{-11+\sqrt{193}}{-4}
$