6(2x-1)=4/7x

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

6(2x-1)=4/7x

We move all terms to the left:

6(2x-1)-(4/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

12x-(+4/7x)-6=0

We get rid of parentheses

12x-4/7x-6=0

We multiply all the terms by the denominator


12x*7x-6*7x-4=0

Wy multiply elements

84x^2-42x-4=0

a = 84; b = -42; c = -4;
Δ = b2-4ac
Δ = -422-4·84·(-4)
Δ = 3108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{777}}{2*84}=\frac{42-2\sqrt{777}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{777}}{2*84}=\frac{42+2\sqrt{777}}{168}
$