3/4x+6=3/7x+3

Solution for 3/4x+6=3/7x+3 equation:

3/4x+6=3/7x+3

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x+3)!=0

x∈R


We get rid of parentheses

3/4x-3/7x-3+6=0

We calculate fractions


21x/28x^2+(-12x)/28x^2-3+6=0

We add all the numbers together, and all the variables

21x/28x^2+(-12x)/28x^2+3=0

We multiply all the terms by the denominator


21x+(-12x)+3*28x^2=0

Wy multiply elements

84x^2+21x+(-12x)=0

We get rid of parentheses

84x^2+21x-12x=0

We add all the numbers together, and all the variables

84x^2+9x=0

a = 84; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·84·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*84}=\frac{-18}{168}
=-3/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*84}=\frac{0}{168}
=0
$