X^2+30x+209=2

Solution for X^2+30x+209=2 equation:

X^2+30X+209=2

We move all terms to the left:

X^2+30X+209-(2)=0

We add all the numbers together, and all the variables

X^2+30X+207=0

a = 1; b = 30; c = +207;
Δ = b2-4ac
Δ = 302-4·1·207
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{2}}{2*1}=\frac{-30-6\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{2}}{2*1}=\frac{-30+6\sqrt{2}}{2}
$