x^2+x=-0.1

Solution for x^2+x=-0.1 equation:

x^2+x=-0.1

We move all terms to the left:

x^2+x-(-0.1)=0

We add all the numbers together, and all the variables

x^2+x+0.1=0

a = 1; b = 1; c = +0.1;
Δ = b2-4ac
Δ = 12-4·1·0.1
Δ = 0.6
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{0.6}}{2*1}=\frac{-1-\sqrt{0.6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.6}}{2*1}=\frac{-1+\sqrt{0.6}}{2}
$