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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-6x^2+15x-(6x(x-2))=0


We calculate terms in parentheses: -(6x(x-2)), so:

6x(x-2)

We multiply parentheses

6x^2-12x

Back to the equation:

-(6x^2-12x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-12x^2+27x=0

a = -12; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-12)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-12}=\frac{-54}{-24}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-12}=\frac{0}{-24}
=0
$