3x(x-5)=3x-5(3x-1)

Solution for 3x(x-5)=3x-5(3x-1) equation:

3x(x-5)=3x-5(3x-1)

We move all terms to the left:

3x(x-5)-(3x-5(3x-1))=0

We multiply parentheses

3x^2-15x-(3x-5(3x-1))=0


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

3x-5(3x-1)

We multiply parentheses

3x-15x+5

We add all the numbers together, and all the variables

-12x+5

Back to the equation:

-(-12x+5)


We get rid of parentheses

3x^2-15x+12x-5=0

We add all the numbers together, and all the variables

3x^2-3x-5=0

a = 3; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·3·(-5)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{69}}{2*3}=\frac{3-\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*3}=\frac{3+\sqrt{69}}{6}
$