X-x^2=-18.75

Solution for X-x^2=-18.75 equation:

X-X^2=-18.75

We move all terms to the left:

X-X^2-(-18.75)=0

We add all the numbers together, and all the variables

-1X^2+X+18.75=0

a = -1; b = 1; c = +18.75;
Δ = b2-4ac
Δ = 12-4·(-1)·18.75
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-2\sqrt{19}}{2*-1}=\frac{-1-2\sqrt{19}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+2\sqrt{19}}{2*-1}=\frac{-1+2\sqrt{19}}{-2}
$