1/7x+4=8/9x-2

Solution for 1/7x+4=8/9x-2 equation:

1/7x+4=8/9x-2

We move all terms to the left:

1/7x+4-(8/9x-2)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 9x-2)!=0

x∈R


We get rid of parentheses

1/7x-8/9x+2+4=0

We calculate fractions


9x/63x^2+(-56x)/63x^2+2+4=0

We add all the numbers together, and all the variables

9x/63x^2+(-56x)/63x^2+6=0

We multiply all the terms by the denominator


9x+(-56x)+6*63x^2=0

Wy multiply elements

378x^2+9x+(-56x)=0

We get rid of parentheses

378x^2+9x-56x=0

We add all the numbers together, and all the variables

378x^2-47x=0

a = 378; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·378·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*378}=\frac{0}{756}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*378}=\frac{94}{756}
=47/378
$