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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

5+x(x+5)

determiningTheFunctionDomain
x(x+5)+5

We multiply parentheses

x^2+5x+5

Back to the equation:

-(x^2+5x+5)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+4x+67=0

a = -1; b = 4; c = +67;
Δ = b2-4ac
Δ = 42-4·(-1)·67
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{71}}{2*-1}=\frac{-4-2\sqrt{71}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{71}}{2*-1}=\frac{-4+2\sqrt{71}}{-2}
$