x^2+2x=12.5

Solution for x^2+2x=12.5 equation:

x^2+2x=12.5

We move all terms to the left:

x^2+2x-(12.5)=0

We add all the numbers together, and all the variables

x^2+2x-12.5=0

a = 1; b = 2; c = -12.5;
Δ = b2-4ac
Δ = 22-4·1·(-12.5)
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-3\sqrt{6}}{2*1}=\frac{-2-3\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+3\sqrt{6}}{2*1}=\frac{-2+3\sqrt{6}}{2}
$