(x+8)(x)/2=209

Solution for (x+8)(x)/2=209 equation:

(x+8)(x)/2=209

We move all terms to the left:

(x+8)(x)/2-(209)=0

We multiply all the terms by the denominator


(x+8)x-209*2=0

We add all the numbers together, and all the variables

(x+8)x-418=0

We multiply parentheses

x^2+8x-418=0

a = 1; b = 8; c = -418;
Δ = b2-4ac
Δ = 82-4·1·(-418)
Δ = 1736
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:

$\sqrt{\Delta}=\sqrt{1736}=\sqrt{4*434}=\sqrt{4}*\sqrt{434}=2\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{434}}{2*1}=\frac{-8-2\sqrt{434}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{434}}{2*1}=\frac{-8+2\sqrt{434}}{2}
$