3x+2=x+4(x2)

Solution for 3x+2=x+4(x2) equation:

3x+2=x+4(x2)

We move all terms to the left:

3x+2-(x+4(x2))=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-4)·2
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{-(2)-6}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-4}=\frac{4}{-8}
=-1/2
$