2x(x-2)=9x(x-1)

Solution for 2x(x-2)=9x(x-1) equation:

2x(x-2)=9x(x-1)

We move all terms to the left:

2x(x-2)-(9x(x-1))=0

We multiply parentheses

2x^2-4x-(9x(x-1))=0


We calculate terms in parentheses: -(9x(x-1)), so:

9x(x-1)

We multiply parentheses

9x^2-9x

Back to the equation:

-(9x^2-9x)


We get rid of parentheses

2x^2-9x^2-4x+9x=0

We add all the numbers together, and all the variables

-7x^2+5x=0

a = -7; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-7)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-7}=\frac{-10}{-14}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-7}=\frac{0}{-14}
=0
$