6x(3x-1)=7x(4x+2)

Solution for 6x(3x-1)=7x(4x+2) equation:

6x(3x-1)=7x(4x+2)

We move all terms to the left:

6x(3x-1)-(7x(4x+2))=0

We multiply parentheses

18x^2-6x-(7x(4x+2))=0


We calculate terms in parentheses: -(7x(4x+2)), so:

7x(4x+2)

We multiply parentheses

28x^2+14x

Back to the equation:

-(28x^2+14x)


We get rid of parentheses

18x^2-28x^2-6x-14x=0

We add all the numbers together, and all the variables

-10x^2-20x=0

a = -10; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-10)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-10}=\frac{40}{-20}
=-2
$