2x+x^2=20.5

Solution for 2x+x^2=20.5 equation:

2x+x^2=20.5

We move all terms to the left:

2x+x^2-(20.5)=0

We add all the numbers together, and all the variables

x^2+2x-20.5=0

a = 1; b = 2; c = -20.5;
Δ = b2-4ac
Δ = 22-4·1·(-20.5)
Δ = 86
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-\sqrt{86}}{2*1}=\frac{-2-\sqrt{86}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{86}}{2*1}=\frac{-2+\sqrt{86}}{2}
$