x^2+x=18.5

Solution for x^2+x=18.5 equation:

x^2+x=18.5

We move all terms to the left:

x^2+x-(18.5)=0

We add all the numbers together, and all the variables

x^2+x-18.5=0

a = 1; b = 1; c = -18.5;
Δ = b2-4ac
Δ = 12-4·1·(-18.5)
Δ = 75
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:

$\sqrt{\Delta}=\sqrt{75}=\sqrt{25*3}=\sqrt{25}*\sqrt{3}=5\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{3}}{2*1}=\frac{-1-5\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{3}}{2*1}=\frac{-1+5\sqrt{3}}{2}
$