/9x+1=7x+19

Solution for /9x+1=7x+19 equation:

/9x+1=7x+19

We move all terms to the left:

/9x+1-(7x+19)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

/9x-7x-19+1=0

We multiply all the terms by the denominator


-7x*9x-19*9x+1*9x+=0

We add all the numbers together, and all the variables

-7x*9x-19*9x+1*9x=0

Wy multiply elements

-63x^2-171x+9x=0

We add all the numbers together, and all the variables

-63x^2-162x=0

a = -63; b = -162; c = 0;
Δ = b2-4ac
Δ = -1622-4·(-63)·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-162}{2*-63}=\frac{0}{-126}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+162}{2*-63}=\frac{324}{-126}
=-2+4/7
$