x+x^2=0.53

Solution for x+x^2=0.53 equation:

x+x^2=0.53

We move all terms to the left:

x+x^2-(0.53)=0

We add all the numbers together, and all the variables

x^2+x-0.53=0

a = 1; b = 1; c = -0.53;
Δ = b2-4ac
Δ = 12-4·1·(-0.53)
Δ = 3.12
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{3.12}}{2*1}=\frac{-1-\sqrt{3.12}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3.12}}{2*1}=\frac{-1+\sqrt{3.12}}{2}
$