6(2x/3)=2(4x/7)

Solution for 6(2x/3)=2(4x/7) equation:

6(2x/3)=2(4x/7)

We move all terms to the left:

6(2x/3)-(2(4x/7))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

12x-(2(+4x/7))=0

We multiply all the terms by the denominator


12x*7))-(2(+4x=0

We add all the numbers together, and all the variables

4x+12x*7))-(2(=0

Wy multiply elements

84x^2+4x=0

a = 84; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·84·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*84}=\frac{-8}{168}
=-1/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*84}=\frac{0}{168}
=0
$