5(2x+8)8x=40

Solution for 5(2x+8)8x=40 equation:

5(2x+8)8x=40

We move all terms to the left:

5(2x+8)8x-(40)=0

We multiply parentheses

80x^2+320x-40=0

a = 80; b = 320; c = -40;
Δ = b2-4ac
Δ = 3202-4·80·(-40)
Δ = 115200
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:

$\sqrt{\Delta}=\sqrt{115200}=\sqrt{57600*2}=\sqrt{57600}*\sqrt{2}=240\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-240\sqrt{2}}{2*80}=\frac{-320-240\sqrt{2}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+240\sqrt{2}}{2*80}=\frac{-320+240\sqrt{2}}{160}
$