X^2-x=-0.13

Solution for X^2-x=-0.13 equation:

X^2-X=-0.13

We move all terms to the left:

X^2-X-(-0.13)=0

We add all the numbers together, and all the variables

X^2-1X+0.13=0

a = 1; b = -1; c = +0.13;
Δ = b2-4ac
Δ = -12-4·1·0.13
Δ = 0.48
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{0.48}}{2*1}=\frac{1-\sqrt{0.48}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{0.48}}{2*1}=\frac{1+\sqrt{0.48}}{2}
$