3(2x+6)8x=46

Solution for 3(2x+6)8x=46 equation:

3(2x+6)8x=46

We move all terms to the left:

3(2x+6)8x-(46)=0

We multiply parentheses

48x^2+144x-46=0

a = 48; b = 144; c = -46;
Δ = b2-4ac
Δ = 1442-4·48·(-46)
Δ = 29568
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:

$\sqrt{\Delta}=\sqrt{29568}=\sqrt{64*462}=\sqrt{64}*\sqrt{462}=8\sqrt{462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-8\sqrt{462}}{2*48}=\frac{-144-8\sqrt{462}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+8\sqrt{462}}{2*48}=\frac{-144+8\sqrt{462}}{96}
$