3x(4x+4)=8(27)

Solution for 3x(4x+4)=8(27) equation:

3x(4x+4)=8(27)

We move all terms to the left:

3x(4x+4)-(8(27))=0

determiningTheFunctionDomain
3x(4x+4)-827=0

We multiply parentheses

12x^2+12x-827=0

a = 12; b = 12; c = -827;
Δ = b2-4ac
Δ = 122-4·12·(-827)
Δ = 39840
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:

$\sqrt{\Delta}=\sqrt{39840}=\sqrt{16*2490}=\sqrt{16}*\sqrt{2490}=4\sqrt{2490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{2490}}{2*12}=\frac{-12-4\sqrt{2490}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{2490}}{2*12}=\frac{-12+4\sqrt{2490}}{24}
$