4/7x=(1+6x)/9

Solution for 4/7x=(1+6x)/9 equation:

4/7x=(1+6x)/9

We move all terms to the left:

4/7x-((1+6x)/9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

4/7x-((6x+1)/9)=0

We calculate fractions


()/63x^2+(-((6x+1)*7x)/63x^2=0

We multiply all the terms by the denominator


(-((6x+1)*7x)+()=0


We calculate terms in parentheses: +(-((6x+1)*7x)+(), so:

-((6x+1)*7x)+(

We add all the numbers together, and all the variables

-((6x+1)*7x)


We calculate terms in parentheses: -((6x+1)*7x), so:

(6x+1)*7x

We multiply parentheses

42x^2+7x

Back to the equation:

-(42x^2+7x)


We get rid of parentheses

-42x^2-7x

Back to the equation:

+(-42x^2-7x)


We get rid of parentheses

-42x^2-7x=0

a = -42; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-42)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-42}=\frac{0}{-84}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-42}=\frac{14}{-84}
=-1/6
$