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

Solution for 2(3+x)-3(x-2)x=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-3x^2+8x+6=0

a = -3; b = 8; c = +6;
Δ = b2-4ac
Δ = 82-4·(-3)·6
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*-3}=\frac{-8-2\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*-3}=\frac{-8+2\sqrt{34}}{-6}
$