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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(x^2-3(-1x+1)), so:

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+x-3x+3+9=0

We add all the numbers together, and all the variables

-1x^2-2x+12=0

a = -1; b = -2; c = +12;
Δ = b2-4ac
Δ = -22-4·(-1)·12
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-1}=\frac{2-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-1}=\frac{2+2\sqrt{13}}{-2}
$