8x=9x(4+x)

Solution for 8x=9x(4+x) equation:

8x=9x(4+x)

We move all terms to the left:

8x-(9x(4+x))=0

We add all the numbers together, and all the variables

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

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

We add all the numbers together, and all the variables

-9x^2-28x=0

a = -9; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-9)·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*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-9}=\frac{56}{-18}
=-3+1/9
$