3x=6x(x-5)

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

3x=6x(x-5)

We move all terms to the left:

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


We calculate terms in parentheses: -(6x(x-5)), so:

6x(x-5)

We multiply parentheses

6x^2-30x

Back to the equation:

-(6x^2-30x)


We get rid of parentheses

-6x^2+3x+30x=0

We add all the numbers together, and all the variables

-6x^2+33x=0

a = -6; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-6)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-6}=\frac{-66}{-12}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-6}=\frac{0}{-12}
=0
$