(x+6+9)*(x+6)=(2x)^2

Solution for (x+6+9)*(x+6)=(2x)^2 equation:

(x+6+9)(x+6)=(2x)^2

We move all terms to the left:

(x+6+9)(x+6)-((2x)^2)=0

determiningTheFunctionDomain
(x+6+9)(x+6)-2x^2=0

We add all the numbers together, and all the variables

-2x^2+(x+15)(x+6)=0

We multiply parentheses ..

-2x^2+(+x^2+6x+15x+90)=0

We get rid of parentheses

-2x^2+x^2+6x+15x+90=0

We add all the numbers together, and all the variables

-1x^2+21x+90=0

a = -1; b = 21; c = +90;
Δ = b2-4ac
Δ = 212-4·(-1)·90
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{89}}{2*-1}=\frac{-21-3\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{89}}{2*-1}=\frac{-21+3\sqrt{89}}{-2}
$