x(7x+2)=2x^2-2x+1

Solution for x(7x+2)=2x^2-2x+1 equation:

x(7x+2)=2x^2-2x+1

We move all terms to the left:

x(7x+2)-(2x^2-2x+1)=0

We multiply parentheses

7x^2+2x-(2x^2-2x+1)=0

We get rid of parentheses

7x^2-2x^2+2x+2x-1=0

We add all the numbers together, and all the variables

5x^2+4x-1=0

a = 5; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·5·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*5}=\frac{2}{10}
=1/5
$