(x)(x+3)=209

Solution for (x)(x+3)=209 equation:

(x)(x+3)=209

We move all terms to the left:

(x)(x+3)-(209)=0

We multiply parentheses

x^2+3x-209=0

a = 1; b = 3; c = -209;
Δ = b2-4ac
Δ = 32-4·1·(-209)
Δ = 845
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:

$\sqrt{\Delta}=\sqrt{845}=\sqrt{169*5}=\sqrt{169}*\sqrt{5}=13\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13\sqrt{5}}{2*1}=\frac{-3-13\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13\sqrt{5}}{2*1}=\frac{-3+13\sqrt{5}}{2}
$