4/7x=3x

Solution for 4/7x=3x equation:

4/7x=3x

We move all terms to the left:

4/7x-(3x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+4/7x=0

We multiply all the terms by the denominator


-3x*7x+4=0

Wy multiply elements

-21x^2+4=0

a = -21; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-21)·4
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*-21}=\frac{0-4\sqrt{21}}{-42}
=-\frac{4\sqrt{21}}{-42}
=-\frac{2\sqrt{21}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*-21}=\frac{0+4\sqrt{21}}{-42}
=\frac{4\sqrt{21}}{-42}
=\frac{2\sqrt{21}}{-21}
$