7/x+4=3/9x+8

Solution for 7/x+4=3/9x+8 equation:

7/x+4=3/9x+8

We move all terms to the left:

7/x+4-(3/9x+8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x+8)!=0

x∈R


We get rid of parentheses

7/x-3/9x-8+4=0

We calculate fractions


63x/9x^2+(-3x)/9x^2-8+4=0

We add all the numbers together, and all the variables

63x/9x^2+(-3x)/9x^2-4=0

We multiply all the terms by the denominator


63x+(-3x)-4*9x^2=0

Wy multiply elements

-36x^2+63x+(-3x)=0

We get rid of parentheses

-36x^2+63x-3x=0

We add all the numbers together, and all the variables

-36x^2+60x=0

a = -36; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-36)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-36}=\frac{-120}{-72}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-36}=\frac{0}{-72}
=0
$