6*x+9=(x+3)2-x2

Solution for 6*x+9=(x+3)2-x2 equation:

6x+9=(x+3)2-x2

We move all terms to the left:

6x+9-((x+3)2-x2)=0


We calculate terms in parentheses: -((x+3)2-x2), so:

(x+3)2-x2

We add all the numbers together, and all the variables

-1x^2+(x+3)2

We multiply parentheses

-1x^2+2x+6

Back to the equation:

-(-1x^2+2x+6)


We get rid of parentheses

1x^2-2x+6x-6+9=0

We add all the numbers together, and all the variables

x^2+4x+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$