10-3/7x=9-4/14x

Solution for 10-3/7x=9-4/14x equation:

10-3/7x=9-4/14x

We move all terms to the left:

10-3/7x-(9-4/14x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/7x-(-4/14x+9)+10=0

We get rid of parentheses

-3/7x+4/14x-9+10=0

We calculate fractions


(-42x)/98x^2+28x/98x^2-9+10=0

We add all the numbers together, and all the variables

(-42x)/98x^2+28x/98x^2+1=0

We multiply all the terms by the denominator


(-42x)+28x+1*98x^2=0

We add all the numbers together, and all the variables

28x+(-42x)+1*98x^2=0

Wy multiply elements

98x^2+28x+(-42x)=0

We get rid of parentheses

98x^2+28x-42x=0

We add all the numbers together, and all the variables

98x^2-14x=0

a = 98; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·98·0
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*98}=\frac{0}{196}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*98}=\frac{28}{196}
=1/7
$