9x(3x-6)=x(5-9x)

Solution for 9x(3x-6)=x(5-9x) equation:

9x(3x-6)=x(5-9x)

We move all terms to the left:

9x(3x-6)-(x(5-9x))=0

We add all the numbers together, and all the variables

9x(3x-6)-(x(-9x+5))=0

We multiply parentheses

27x^2-54x-(x(-9x+5))=0


We calculate terms in parentheses: -(x(-9x+5)), so:

x(-9x+5)

We multiply parentheses

-9x^2+5x

Back to the equation:

-(-9x^2+5x)


We get rid of parentheses

27x^2+9x^2-5x-54x=0

We add all the numbers together, and all the variables

36x^2-59x=0

a = 36; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·36·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*36}=\frac{118}{72}
=1+23/36
$