(X+3)2=x2+5

Solution for (X+3)2=x2+5 equation:

(X+3)2=X2+5

We move all terms to the left:

(X+3)2-(X2+5)=0

We add all the numbers together, and all the variables

-(+X^2+5)+(X+3)2=0

We multiply parentheses

-(+X^2+5)+2X+6=0

We get rid of parentheses

-X^2+2X-5+6=0

We add all the numbers together, and all the variables

-1X^2+2X+1=0

a = -1; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-1)·1
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2}}{2*-1}=\frac{-2-2\sqrt{2}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2}}{2*-1}=\frac{-2+2\sqrt{2}}{-2}
$