A=x^2-18x=80

Solution for A=x^2-18x=80 equation:

=A^2-18A=80

We move all terms to the left:

-(A^2-18A)=0

We get rid of parentheses

-A^2+18A=0

We add all the numbers together, and all the variables

-1A^2+18A=0

a = -1; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-1)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-1}=\frac{-36}{-2}
=+18
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-1}=\frac{0}{-2}
=0
$