x/7x-9=3x+19

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

x/7x-9=3x+19

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x-3x*7x-19*7x-9*7x=0

Wy multiply elements

-21x^2+x-133x-63x=0

We add all the numbers together, and all the variables

-21x^2-195x=0

a = -21; b = -195; c = 0;
Δ = b2-4ac
Δ = -1952-4·(-21)·0
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-195)-195}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+195}{2*-21}=\frac{390}{-42}
=-9+2/7
$