6x(12+x)=54

Solution for 6x(12+x)=54 equation:

6x(12+x)=54

We move all terms to the left:

6x(12+x)-(54)=0

We add all the numbers together, and all the variables

6x(x+12)-54=0

We multiply parentheses

6x^2+72x-54=0

a = 6; b = 72; c = -54;
Δ = b2-4ac
Δ = 722-4·6·(-54)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-36\sqrt{5}}{2*6}=\frac{-72-36\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+36\sqrt{5}}{2*6}=\frac{-72+36\sqrt{5}}{12}
$