9(8+x)=5+x(x+9)

Solution for 9(8+x)=5+x(x+9) equation:

9(8+x)=5+x(x+9)

We move all terms to the left:

9(8+x)-(5+x(x+9))=0

We add all the numbers together, and all the variables

9(x+8)-(5+x(x+9))=0

We multiply parentheses

9x-(5+x(x+9))+72=0


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

5+x(x+9)

determiningTheFunctionDomain
x(x+9)+5

We multiply parentheses

x^2+9x+5

Back to the equation:

-(x^2+9x+5)


We get rid of parentheses

-x^2+9x-9x-5+72=0

We add all the numbers together, and all the variables

-1x^2+67=0

a = -1; b = 0; c = +67;
Δ = b2-4ac
Δ = 02-4·(-1)·67
Δ = 268
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{67}}{2*-1}=\frac{0-2\sqrt{67}}{-2}
=-\frac{2\sqrt{67}}{-2}
=-\frac{\sqrt{67}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{67}}{2*-1}=\frac{0+2\sqrt{67}}{-2}
=\frac{2\sqrt{67}}{-2}
=\frac{\sqrt{67}}{-1}
$