2(3x-6)=3(5-x)x

Solution for 2(3x-6)=3(5-x)x equation:

2(3x-6)=3(5-x)x

We move all terms to the left:

2(3x-6)-(3(5-x)x)=0

We add all the numbers together, and all the variables

2(3x-6)-(3(-1x+5)x)=0

We multiply parentheses

6x-(3(-1x+5)x)-12=0


We calculate terms in parentheses: -(3(-1x+5)x), so:

3(-1x+5)x

We multiply parentheses

-3x^2+15x

Back to the equation:

-(-3x^2+15x)


We get rid of parentheses

3x^2-15x+6x-12=0

We add all the numbers together, and all the variables

3x^2-9x-12=0

a = 3; b = -9; c = -12;
Δ = b2-4ac
Δ = -92-4·3·(-12)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*3}=\frac{24}{6}
=4
$