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

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

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

We move all terms to the left:

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

We multiply parentheses

16x-(8x(-3x-2)+8)+4+2=0


We calculate terms in parentheses: -(8x(-3x-2)+8), so:

8x(-3x-2)+8

We multiply parentheses

-24x^2-16x+8

Back to the equation:

-(-24x^2-16x+8)


We add all the numbers together, and all the variables

-(-24x^2-16x+8)+16x+6=0

We get rid of parentheses

24x^2+16x+16x-8+6=0

We add all the numbers together, and all the variables

24x^2+32x-2=0

a = 24; b = 32; c = -2;
Δ = b2-4ac
Δ = 322-4·24·(-2)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{19}}{2*24}=\frac{-32-8\sqrt{19}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{19}}{2*24}=\frac{-32+8\sqrt{19}}{48}
$