x+x^2=87.75

Solution for x+x^2=87.75 equation:

x+x^2=87.75

We move all terms to the left:

x+x^2-(87.75)=0

We add all the numbers together, and all the variables

x^2+x-87.75=0

a = 1; b = 1; c = -87.75;
Δ = b2-4ac
Δ = 12-4·1·(-87.75)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-4\sqrt{22}}{2*1}=\frac{-1-4\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+4\sqrt{22}}{2*1}=\frac{-1+4\sqrt{22}}{2}
$