2(x-1)(5x+2)=2x

Solution for 2(x-1)(5x+2)=2x equation:

2(x-1)(5x+2)=2x

We move all terms to the left:

2(x-1)(5x+2)-(2x)=0

We add all the numbers together, and all the variables

-2x+2(x-1)(5x+2)=0

We multiply parentheses ..

2(+5x^2+2x-5x-2)-2x=0

We multiply parentheses

10x^2+4x-10x-2x-4=0

We add all the numbers together, and all the variables

10x^2-8x-4=0

a = 10; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·10·(-4)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{14}}{2*10}=\frac{8-4\sqrt{14}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{14}}{2*10}=\frac{8+4\sqrt{14}}{20}
$