8x(2+4x)=46

Solution for 8x(2+4x)=46 equation:

8x(2+4x)=46

We move all terms to the left:

8x(2+4x)-(46)=0

We add all the numbers together, and all the variables

8x(4x+2)-46=0

We multiply parentheses

32x^2+16x-46=0

a = 32; b = 16; c = -46;
Δ = b2-4ac
Δ = 162-4·32·(-46)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-32\sqrt{6}}{2*32}=\frac{-16-32\sqrt{6}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+32\sqrt{6}}{2*32}=\frac{-16+32\sqrt{6}}{64}
$