(2x-1+4x^2)2=x

Solution for (2x-1+4x^2)2=x equation:

(2x-1+4x^2)2=x

We move all terms to the left:

(2x-1+4x^2)2-(x)=0

We add all the numbers together, and all the variables

(2x-1+4x^2)2-1x=0

We multiply parentheses

8x^2+4x-1x-2=0

We add all the numbers together, and all the variables

8x^2+3x-2=0

a = 8; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·8·(-2)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{73}}{2*8}=\frac{-3-\sqrt{73}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{73}}{2*8}=\frac{-3+\sqrt{73}}{16}
$