X^2-x=0.06

Solution for X^2-x=0.06 equation:

X^2-X=0.06

We move all terms to the left:

X^2-X-(0.06)=0

We add all the numbers together, and all the variables

X^2-1X-0.06=0

a = 1; b = -1; c = -0.06;
Δ = b2-4ac
Δ = -12-4·1·(-0.06)
Δ = 1.24
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{1.24}}{2*1}=\frac{1-\sqrt{1.24}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.24}}{2*1}=\frac{1+\sqrt{1.24}}{2}
$