9+3/10x=7/19x

Solution for 9+3/10x=7/19x equation:

9+3/10x=7/19x

We move all terms to the left:

9+3/10x-(7/19x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 19x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/10x-(+7/19x)+9=0

We get rid of parentheses

3/10x-7/19x+9=0

We calculate fractions


57x/190x^2+(-70x)/190x^2+9=0

We multiply all the terms by the denominator


57x+(-70x)+9*190x^2=0

Wy multiply elements

1710x^2+57x+(-70x)=0

We get rid of parentheses

1710x^2+57x-70x=0

We add all the numbers together, and all the variables

1710x^2-13x=0

a = 1710; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·1710·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*1710}=\frac{0}{3420}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*1710}=\frac{26}{3420}
=13/1710
$