x+3(x+3)=x(7+x)

Solution for x+3(x+3)=x(7+x) equation:

x+3(x+3)=x(7+x)

We move all terms to the left:

x+3(x+3)-(x(7+x))=0

We add all the numbers together, and all the variables

x+3(x+3)-(x(x+7))=0

We multiply parentheses

x+3x-(x(x+7))+9=0


We calculate terms in parentheses: -(x(x+7)), so:

x(x+7)

We multiply parentheses

x^2+7x

Back to the equation:

-(x^2+7x)


We add all the numbers together, and all the variables

4x-(x^2+7x)+9=0

We get rid of parentheses

-x^2+4x-7x+9=0

We add all the numbers together, and all the variables

-1x^2-3x+9=0

a = -1; b = -3; c = +9;
Δ = b2-4ac
Δ = -32-4·(-1)·9
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*-1}=\frac{3-3\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*-1}=\frac{3+3\sqrt{5}}{-2}
$