(X)2+(x+3)2=225

Solution for (X)2+(x+3)2=225 equation:

(X)2+(X+3)2=225

We move all terms to the left:

(X)2+(X+3)2-(225)=0

We add all the numbers together, and all the variables

X^2+(X+3)2-225=0

We multiply parentheses

X^2+2X+6-225=0

We add all the numbers together, and all the variables

X^2+2X-219=0

a = 1; b = 2; c = -219;
Δ = b2-4ac
Δ = 22-4·1·(-219)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{55}}{2*1}=\frac{-2-4\sqrt{55}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{55}}{2*1}=\frac{-2+4\sqrt{55}}{2}
$