3x+2=4x^2+2x+1

Solution for 3x+2=4x^2+2x+1 equation:

3x+2=4x^2+2x+1

We move all terms to the left:

3x+2-(4x^2+2x+1)=0

We get rid of parentheses

-4x^2+3x-2x-1+2=0

We add all the numbers together, and all the variables

-4x^2+x+1=0

a = -4; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-4)·1
Δ = 17
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{-(1)-\sqrt{17}}{2*-4}=\frac{-1-\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-4}=\frac{-1+\sqrt{17}}{-8}
$