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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3x(x-2)), so:

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+2x+6x+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}
$