X=x^2-1.5

Solution for X=x^2-1.5 equation:

X=X^2-1.5

We move all terms to the left:

X-(X^2-1.5)=0

We get rid of parentheses

-X^2+X+1.5=0

We add all the numbers together, and all the variables

-1X^2+X+1.5=0

a = -1; b = 1; c = +1.5;
Δ = b2-4ac
Δ = 12-4·(-1)·1.5
Δ = 7
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{7}}{2*-1}=\frac{-1-\sqrt{7}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{7}}{2*-1}=\frac{-1+\sqrt{7}}{-2}
$