2x(x-4)=9x(x-4)

Solution for 2x(x-4)=9x(x-4) equation:

2x(x-4)=9x(x-4)

We move all terms to the left:

2x(x-4)-(9x(x-4))=0

We multiply parentheses

2x^2-8x-(9x(x-4))=0


We calculate terms in parentheses: -(9x(x-4)), so:

9x(x-4)

We multiply parentheses

9x^2-36x

Back to the equation:

-(9x^2-36x)


We get rid of parentheses

2x^2-9x^2-8x+36x=0

We add all the numbers together, and all the variables

-7x^2+28x=0

a = -7; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-7)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-7}=\frac{-56}{-14}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-7}=\frac{0}{-14}
=0
$