x2+6x-209=0

Solution for x2+6x-209=0 equation:

x2+6x-209=0

We add all the numbers together, and all the variables

x^2+6x-209=0

a = 1; b = 6; c = -209;
Δ = b2-4ac
Δ = 62-4·1·(-209)
Δ = 872
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:

$\sqrt{\Delta}=\sqrt{872}=\sqrt{4*218}=\sqrt{4}*\sqrt{218}=2\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{218}}{2*1}=\frac{-6-2\sqrt{218}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{218}}{2*1}=\frac{-6+2\sqrt{218}}{2}
$