0=(-x^2)+x+2

Solution for 0=(-x^2)+x+2 equation:

0=(-x^2)+x+2

We move all terms to the left:

0-((-x^2)+x+2)=0

We add all the numbers together, and all the variables

-((-x^2)+x+2)=0


We calculate terms in parentheses: -((-x^2)+x+2), so:

(-x^2)+x+2

We get rid of parentheses

-x^2+x+2

We add all the numbers together, and all the variables

-1x^2+x+2

Back to the equation:

-(-1x^2+x+2)


We get rid of parentheses

1x^2-x-2=0

We add all the numbers together, and all the variables

x^2-1x-2=0

a = 1; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·1·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*1}=\frac{4}{2}
=2
$