(X+3)2+(2x)2=36

Solution for (X+3)2+(2x)2=36 equation:

(X+3)2+(2X)2=36

We move all terms to the left:

(X+3)2+(2X)2-(36)=0

We add all the numbers together, and all the variables

2X^2+(X+3)2-36=0

We multiply parentheses

2X^2+2X+6-36=0

We add all the numbers together, and all the variables

2X^2+2X-30=0

a = 2; b = 2; c = -30;
Δ = b2-4ac
Δ = 22-4·2·(-30)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*2}=\frac{-2-2\sqrt{61}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*2}=\frac{-2+2\sqrt{61}}{4}
$