4(8-5x)2x=-40

Solution for 4(8-5x)2x=-40 equation:

4(8-5x)2x=-40

We move all terms to the left:

4(8-5x)2x-(-40)=0

We add all the numbers together, and all the variables

4(-5x+8)2x-(-40)=0

We add all the numbers together, and all the variables

4(-5x+8)2x+40=0

We multiply parentheses

-40x^2+64x+40=0

a = -40; b = 64; c = +40;
Δ = b2-4ac
Δ = 642-4·(-40)·40
Δ = 10496
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:

$\sqrt{\Delta}=\sqrt{10496}=\sqrt{256*41}=\sqrt{256}*\sqrt{41}=16\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{41}}{2*-40}=\frac{-64-16\sqrt{41}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{41}}{2*-40}=\frac{-64+16\sqrt{41}}{-80}
$