3/7x-4=4/3x-8

Solution for 3/7x-4=4/3x-8 equation:

3/7x-4=4/3x-8

We move all terms to the left:

3/7x-4-(4/3x-8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

3/7x-4/3x+8-4=0

We calculate fractions


9x/21x^2+(-28x)/21x^2+8-4=0

We add all the numbers together, and all the variables

9x/21x^2+(-28x)/21x^2+4=0

We multiply all the terms by the denominator


9x+(-28x)+4*21x^2=0

Wy multiply elements

84x^2+9x+(-28x)=0

We get rid of parentheses

84x^2+9x-28x=0

We add all the numbers together, and all the variables

84x^2-19x=0

a = 84; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·84·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*84}=\frac{0}{168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*84}=\frac{38}{168}
=19/84
$