-4(2x+4)3x+2=-44

Solution for -4(2x+4)3x+2=-44 equation:

-4(2x+4)3x+2=-44

We move all terms to the left:

-4(2x+4)3x+2-(-44)=0

We add all the numbers together, and all the variables

-4(2x+4)3x+46=0

We multiply parentheses

-24x^2-48x+46=0

a = -24; b = -48; c = +46;
Δ = b2-4ac
Δ = -482-4·(-24)·46
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{105}}{2*-24}=\frac{48-8\sqrt{105}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{105}}{2*-24}=\frac{48+8\sqrt{105}}{-48}
$