9x(x-16)=16(1-9x)

Solution for 9x(x-16)=16(1-9x) equation:

9x(x-16)=16(1-9x)

We move all terms to the left:

9x(x-16)-(16(1-9x))=0

We add all the numbers together, and all the variables

9x(x-16)-(16(-9x+1))=0

We multiply parentheses

9x^2-144x-(16(-9x+1))=0


We calculate terms in parentheses: -(16(-9x+1)), so:

16(-9x+1)

We multiply parentheses

-144x+16

Back to the equation:

-(-144x+16)


We get rid of parentheses

9x^2-144x+144x-16=0

We add all the numbers together, and all the variables

9x^2-16=0

a = 9; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·9·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*9}=\frac{-24}{18}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*9}=\frac{24}{18}
=1+1/3
$