(x+3)2=x2-3(1-x)

Solution for (x+3)2=x2-3(1-x) equation:

(x+3)2=x2-3(1-x)

We move all terms to the left:

(x+3)2-(x2-3(1-x))=0

We add all the numbers together, and all the variables

(x+3)2-(x2-3(-1x+1))=0

We multiply parentheses

2x-(x2-3(-1x+1))+6=0


We calculate terms in parentheses: -(x2-3(-1x+1)), so:

x2-3(-1x+1)

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2+3x-3

Back to the equation:

-(x^2+3x-3)


We get rid of parentheses

-x^2+2x-3x+3+6=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +9;
Δ = b2-4ac
Δ = -12-4·(-1)·9
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{37}}{2*-1}=\frac{1-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{37}}{2*-1}=\frac{1+\sqrt{37}}{-2}
$