A=x2-x-3

Solution for A=x2-x-3 equation:

=A2-A-3

We move all terms to the left:

-(A2-A-3)=0

We add all the numbers together, and all the variables

-(+A^2-1A-3)=0

We get rid of parentheses

-A^2+1A+3=0

We add all the numbers together, and all the variables

-1A^2+A+3=0

a = -1; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-1)·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{13}}{2*-1}=\frac{-1-\sqrt{13}}{-2}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*-1}=\frac{-1+\sqrt{13}}{-2}
$