7/x-5/6=7/9x-4

Solution for 7/x-5/6=7/9x-4 equation:

7/x-5/6=7/9x-4

We move all terms to the left:

7/x-5/6-(7/9x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x-4)!=0

x∈R


We get rid of parentheses

7/x-7/9x+4-5/6=0

We calculate fractions


(-405x^2)/324x^2+2268x/324x^2+(-252x)/324x^2+4=0

We multiply all the terms by the denominator


(-405x^2)+2268x+(-252x)+4*324x^2=0

Wy multiply elements

(-405x^2)+1296x^2+2268x+(-252x)=0

We get rid of parentheses

-405x^2+1296x^2+2268x-252x=0

We add all the numbers together, and all the variables

891x^2+2016x=0

a = 891; b = 2016; c = 0;
Δ = b2-4ac
Δ = 20162-4·891·0
Δ = 4064256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4064256}=2016$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2016)-2016}{2*891}=\frac{-4032}{1782}
=-2+26/99
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2016)+2016}{2*891}=\frac{0}{1782}
=0
$