2(-4x+2)5x-2=-19

Solution for 2(-4x+2)5x-2=-19 equation:

2(-4x+2)5x-2=-19

We move all terms to the left:

2(-4x+2)5x-2-(-19)=0

We add all the numbers together, and all the variables

2(-4x+2)5x+17=0

We multiply parentheses

-40x^2+20x+17=0

a = -40; b = 20; c = +17;
Δ = b2-4ac
Δ = 202-4·(-40)·17
Δ = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{195}}{2*-40}=\frac{-20-4\sqrt{195}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{195}}{2*-40}=\frac{-20+4\sqrt{195}}{-80}
$