(3x+2)=9x^2-6x+4

Solution for (3x+2)=9x^2-6x+4 equation:

(3x+2)=9x^2-6x+4

We move all terms to the left:

(3x+2)-(9x^2-6x+4)=0

We get rid of parentheses

-9x^2+3x+6x+2-4=0

We add all the numbers together, and all the variables

-9x^2+9x-2=0

a = -9; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-9)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-9}=\frac{-12}{-18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-9}=\frac{-6}{-18}
=1/3
$