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+80)=0

We get rid of parentheses

-A^2+18A-80=0

We add all the numbers together, and all the variables

-1A^2+18A-80=0

a = -1; b = 18; c = -80;
Δ = b2-4ac
Δ = 182-4·(-1)·(-80)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2}{2*-1}=\frac{-20}{-2}
=+10
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2}{2*-1}=\frac{-16}{-2}
=+8
$