x^2+x=83.5

Solution for x^2+x=83.5 equation:

x^2+x=83.5

We move all terms to the left:

x^2+x-(83.5)=0

We add all the numbers together, and all the variables

x^2+x-83.5=0

a = 1; b = 1; c = -83.5;
Δ = b2-4ac
Δ = 12-4·1·(-83.5)
Δ = 335
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{-(1)-\sqrt{335}}{2*1}=\frac{-1-\sqrt{335}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{335}}{2*1}=\frac{-1+\sqrt{335}}{2}
$