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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+3x^2-6x+4x-8)3-3x-4=0

We multiply parentheses

9x^2-18x+12x-3x-24-4=0

We add all the numbers together, and all the variables

9x^2-9x-28=0

a = 9; b = -9; c = -28;
Δ = b2-4ac
Δ = -92-4·9·(-28)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-33}{2*9}=\frac{-24}{18}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*9}=\frac{42}{18}
=2+1/3
$