9x-13=2x(x-3)

Solution for 9x-13=2x(x-3) equation:

9x-13=2x(x-3)

We move all terms to the left:

9x-13-(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+9x+6x-13=0

We add all the numbers together, and all the variables

-2x^2+15x-13=0

a = -2; b = 15; c = -13;
Δ = b2-4ac
Δ = 152-4·(-2)·(-13)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-11}{2*-2}=\frac{-26}{-4}
=6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+11}{2*-2}=\frac{-4}{-4}
=1
$