-2(x+9)-4x(3-2x)=48

Solution for -2(x+9)-4x(3-2x)=48 equation:

-2(x+9)-4x(3-2x)=48

We move all terms to the left:

-2(x+9)-4x(3-2x)-(48)=0

We add all the numbers together, and all the variables

-2(x+9)-4x(-2x+3)-48=0

We multiply parentheses

8x^2-2x-12x-18-48=0

We add all the numbers together, and all the variables

8x^2-14x-66=0

a = 8; b = -14; c = -66;
Δ = b2-4ac
Δ = -142-4·8·(-66)
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{577}}{2*8}=\frac{14-2\sqrt{577}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{577}}{2*8}=\frac{14+2\sqrt{577}}{16}
$