3/4x-5/7x=9/14

Solution for 3/4x-5/7x=9/14 equation:

3/4x-5/7x=9/14

We move all terms to the left:

3/4x-5/7x-(9/14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-5/7x-(+9/14)=0

We get rid of parentheses

3/4x-5/7x-9/14=0

We calculate fractions


(-1764x^2)/392x^2+294x/392x^2+(-280x)/392x^2=0

We multiply all the terms by the denominator


(-1764x^2)+294x+(-280x)=0

We get rid of parentheses

-1764x^2+294x-280x=0

We add all the numbers together, and all the variables

-1764x^2+14x=0

a = -1764; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-1764)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-1764}=\frac{-28}{-3528}
=1/126
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-1764}=\frac{0}{-3528}
=0
$