2x(-5+8x)+6=40-8x

Solution for 2x(-5+8x)+6=40-8x equation:

2x(-5+8x)+6=40-8x

We move all terms to the left:

2x(-5+8x)+6-(40-8x)=0

We add all the numbers together, and all the variables

2x(8x-5)-(-8x+40)+6=0

We multiply parentheses

16x^2-10x-(-8x+40)+6=0

We get rid of parentheses

16x^2-10x+8x-40+6=0

We add all the numbers together, and all the variables

16x^2-2x-34=0

a = 16; b = -2; c = -34;
Δ = b2-4ac
Δ = -22-4·16·(-34)
Δ = 2180
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:

$\sqrt{\Delta}=\sqrt{2180}=\sqrt{4*545}=\sqrt{4}*\sqrt{545}=2\sqrt{545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{545}}{2*16}=\frac{2-2\sqrt{545}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{545}}{2*16}=\frac{2+2\sqrt{545}}{32}
$