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

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

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

We move all terms to the left:

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


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

3(x-2)2x

We multiply parentheses

6x^2-12x

Back to the equation:

-(6x^2-12x)


We get rid of parentheses

-6x^2+2x+12x+3=0

We add all the numbers together, and all the variables

-6x^2+14x+3=0

a = -6; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·(-6)·3
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{67}}{2*-6}=\frac{-14-2\sqrt{67}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{67}}{2*-6}=\frac{-14+2\sqrt{67}}{-12}
$