8(2x+5)16x=40

Solution for 8(2x+5)16x=40 equation:

8(2x+5)16x=40

We move all terms to the left:

8(2x+5)16x-(40)=0

We multiply parentheses

256x^2+640x-40=0

a = 256; b = 640; c = -40;
Δ = b2-4ac
Δ = 6402-4·256·(-40)
Δ = 450560
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:

$\sqrt{\Delta}=\sqrt{450560}=\sqrt{4096*110}=\sqrt{4096}*\sqrt{110}=64\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-64\sqrt{110}}{2*256}=\frac{-640-64\sqrt{110}}{512}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+64\sqrt{110}}{2*256}=\frac{-640+64\sqrt{110}}{512}
$