x(x-30)+81=0

Solution for x(x-30)+81=0 equation:

x(x-30)+81=0

We multiply parentheses

x^2-30x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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