3x(x-4)-2(x-5)=6x-2(x-5)

Solution for 3x(x-4)-2(x-5)=6x-2(x-5) equation:

3x(x-4)-2(x-5)=6x-2(x-5)

We move all terms to the left:

3x(x-4)-2(x-5)-(6x-2(x-5))=0

We multiply parentheses

3x^2-12x-2x-(6x-2(x-5))+10=0


We calculate terms in parentheses: -(6x-2(x-5)), so:

6x-2(x-5)

We multiply parentheses

6x-2x+10

We add all the numbers together, and all the variables

4x+10

Back to the equation:

-(4x+10)


We add all the numbers together, and all the variables

3x^2-14x-(4x+10)+10=0

We get rid of parentheses

3x^2-14x-4x-10+10=0

We add all the numbers together, and all the variables

3x^2-18x=0

a = 3; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·3·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*3}=\frac{36}{6}
=6
$