5-2(3x+8)2x=17

Solution for 5-2(3x+8)2x=17 equation:

5-2(3x+8)2x=17

We move all terms to the left:

5-2(3x+8)2x-(17)=0

We add all the numbers together, and all the variables

-2(3x+8)2x-12=0

We multiply parentheses

-12x^2-32x-12=0

a = -12; b = -32; c = -12;
Δ = b2-4ac
Δ = -322-4·(-12)·(-12)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{7}}{2*-12}=\frac{32-8\sqrt{7}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{7}}{2*-12}=\frac{32+8\sqrt{7}}{-24}
$