3/4x-7=14+3/7x

Solution for 3/4x-7=14+3/7x equation:

3/4x-7=14+3/7x

We move all terms to the left:

3/4x-7-(14+3/7x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(3/7x+14)-7=0

We get rid of parentheses

3/4x-3/7x-14-7=0

We calculate fractions


21x/28x^2+(-12x)/28x^2-14-7=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-588x^2+21x+(-12x)=0

We get rid of parentheses

-588x^2+21x-12x=0

We add all the numbers together, and all the variables

-588x^2+9x=0

a = -588; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-588)·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*-588}=\frac{-18}{-1176}
=3/196
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-588}=\frac{0}{-1176}
=0
$