9x(3x+5)=12-(x+9)

Solution for 9x(3x+5)=12-(x+9) equation:

9x(3x+5)=12-(x+9)

We move all terms to the left:

9x(3x+5)-(12-(x+9))=0

We multiply parentheses

27x^2+45x-(12-(x+9))=0


We calculate terms in parentheses: -(12-(x+9)), so:

12-(x+9)

determiningTheFunctionDomain
-(x+9)+12

We get rid of parentheses

-x-9+12

We add all the numbers together, and all the variables

-1x+3

Back to the equation:

-(-1x+3)


We get rid of parentheses

27x^2+45x+1x-3=0

We add all the numbers together, and all the variables

27x^2+46x-3=0

a = 27; b = 46; c = -3;
Δ = b2-4ac
Δ = 462-4·27·(-3)
Δ = 2440
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:

$\sqrt{\Delta}=\sqrt{2440}=\sqrt{4*610}=\sqrt{4}*\sqrt{610}=2\sqrt{610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{610}}{2*27}=\frac{-46-2\sqrt{610}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{610}}{2*27}=\frac{-46+2\sqrt{610}}{54}
$