(x)(x+2)=23.5

Solution for (x)(x+2)=23.5 equation:

(x)(x+2)=23.5

We move all terms to the left:

(x)(x+2)-(23.5)=0

We add all the numbers together, and all the variables

x(x+2)-23.5=0

We multiply parentheses

x^2+2x-23.5=0

a = 1; b = 2; c = -23.5;
Δ = b2-4ac
Δ = 22-4·1·(-23.5)
Δ = 98
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:

$\sqrt{\Delta}=\sqrt{98}=\sqrt{49*2}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-7\sqrt{2}}{2*1}=\frac{-2-7\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+7\sqrt{2}}{2*1}=\frac{-2+7\sqrt{2}}{2}
$