30w-w^2=81

Solution for 30w-w^2=81 equation:

30w-w^2=81

We move all terms to the left:

30w-w^2-(81)=0

We add all the numbers together, and all the variables

-1w^2+30w-81=0

a = -1; b = 30; c = -81;
Δ = b2-4ac
Δ = 302-4·(-1)·(-81)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-24}{2*-1}=\frac{-54}{-2}
=+27
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+24}{2*-1}=\frac{-6}{-2}
=+3
$