A=34w-w^2

Solution for A=34w-w^2 equation:

=34A-A^2

We move all terms to the left:

-(34A-A^2)=0

We get rid of parentheses

A^2-34A=0

a = 1; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·1·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*1}=\frac{68}{2}
=34
$