3x(x-2)=2(x+1)

Solution for 3x(x-2)=2(x+1) equation:

3x(x-2)=2(x+1)

We move all terms to the left:

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

We multiply parentheses

3x^2-6x-(2(x+1))=0


We calculate terms in parentheses: -(2(x+1)), so:

2(x+1)

We multiply parentheses

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

3x^2-6x-2x-2=0

We add all the numbers together, and all the variables

3x^2-8x-2=0

a = 3; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·3·(-2)
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*3}=\frac{8-2\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*3}=\frac{8+2\sqrt{22}}{6}
$