-4(2x+5)8x=-11

Solution for -4(2x+5)8x=-11 equation:

-4(2x+5)8x=-11

We move all terms to the left:

-4(2x+5)8x-(-11)=0

We add all the numbers together, and all the variables

-4(2x+5)8x+11=0

We multiply parentheses

-64x^2-160x+11=0

a = -64; b = -160; c = +11;
Δ = b2-4ac
Δ = -1602-4·(-64)·11
Δ = 28416
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:

$\sqrt{\Delta}=\sqrt{28416}=\sqrt{256*111}=\sqrt{256}*\sqrt{111}=16\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-16\sqrt{111}}{2*-64}=\frac{160-16\sqrt{111}}{-128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+16\sqrt{111}}{2*-64}=\frac{160+16\sqrt{111}}{-128}
$