5(x+2)8x=-8

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

5(x+2)8x=-8

We move all terms to the left:

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

We add all the numbers together, and all the variables

5(x+2)8x+8=0

We multiply parentheses

40x^2+80x+8=0

a = 40; b = 80; c = +8;
Δ = b2-4ac
Δ = 802-4·40·8
Δ = 5120
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:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-32\sqrt{5}}{2*40}=\frac{-80-32\sqrt{5}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+32\sqrt{5}}{2*40}=\frac{-80+32\sqrt{5}}{80}
$