X-x^2=0.065

Solution for X-x^2=0.065 equation:

X-X^2=0.065

We move all terms to the left:

X-X^2-(0.065)=0

We add all the numbers together, and all the variables

-1X^2+X-0.065=0

a = -1; b = 1; c = -0.065;
Δ = b2-4ac
Δ = 12-4·(-1)·(-0.065)
Δ = 0.74
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{0.74}}{2*-1}=\frac{-1-\sqrt{0.74}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.74}}{2*-1}=\frac{-1+\sqrt{0.74}}{-2}
$