(X-x^2)-(2x^2+x-1)=5+2x-3^2

Solution for (X-x^2)-(2x^2+x-1)=5+2x-3^2 equation:

(X-X^2)-(2X^2+X-1)=5+2X-3^2

We move all terms to the left:

(X-X^2)-(2X^2+X-1)-(5+2X-3^2)=0

We get rid of parentheses

-X^2-2X^2+X-X-2X+1-5+3^2=0

We add all the numbers together, and all the variables

-3X^2-2X+5=0

a = -3; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-3)·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-3}=\frac{-6}{-6}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-3}=\frac{10}{-6}
=-1+2/3
$