32=x(x+9)

Solution for 32=x(x+9) equation:

32=x(x+9)

We move all terms to the left:

32-(x(x+9))=0


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

x(x+9)

We multiply parentheses

x^2+9x

Back to the equation:

-(x^2+9x)


We get rid of parentheses

-x^2-9x+32=0

We add all the numbers together, and all the variables

-1x^2-9x+32=0

a = -1; b = -9; c = +32;
Δ = b2-4ac
Δ = -92-4·(-1)·32
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{209}}{2*-1}=\frac{9-\sqrt{209}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{209}}{2*-1}=\frac{9+\sqrt{209}}{-2}
$