6x(x-27)=-84

Solution for 6x(x-27)=-84 equation:

6x(x-27)=-84

We move all terms to the left:

6x(x-27)-(-84)=0

We add all the numbers together, and all the variables

6x(x-27)+84=0

We multiply parentheses

6x^2-162x+84=0

a = 6; b = -162; c = +84;
Δ = b2-4ac
Δ = -1622-4·6·84
Δ = 24228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24228}=\sqrt{36*673}=\sqrt{36}*\sqrt{673}=6\sqrt{673}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-6\sqrt{673}}{2*6}=\frac{162-6\sqrt{673}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+6\sqrt{673}}{2*6}=\frac{162+6\sqrt{673}}{12}
$