6(x^2+78x+216)=0

Solution for 6(x^2+78x+216)=0 equation:

6(x^2+78x+216)=0

We multiply parentheses

6x^2+468x+1296=0

a = 6; b = 468; c = +1296;
Δ = b2-4ac
Δ = 4682-4·6·1296
Δ = 187920
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:

$\sqrt{\Delta}=\sqrt{187920}=\sqrt{1296*145}=\sqrt{1296}*\sqrt{145}=36\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(468)-36\sqrt{145}}{2*6}=\frac{-468-36\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(468)+36\sqrt{145}}{2*6}=\frac{-468+36\sqrt{145}}{12}
$