-9/7x-2/3x+1=2/6

Solution for -9/7x-2/3x+1=2/6 equation:

-9/7x-2/3x+1=2/6

We move all terms to the left:

-9/7x-2/3x+1-(2/6)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-9/7x-2/3x+1-(+2/6)=0

We get rid of parentheses

-9/7x-2/3x+1-2/6=0

We calculate fractions


(-126x^2)/756x^2+(-972x)/756x^2+(-504x)/756x^2+1=0

We multiply all the terms by the denominator


(-126x^2)+(-972x)+(-504x)+1*756x^2=0

Wy multiply elements

(-126x^2)+756x^2+(-972x)+(-504x)=0

We get rid of parentheses

-126x^2+756x^2-972x-504x=0

We add all the numbers together, and all the variables

630x^2-1476x=0

a = 630; b = -1476; c = 0;
Δ = b2-4ac
Δ = -14762-4·630·0
Δ = 2178576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2178576}=1476$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1476)-1476}{2*630}=\frac{0}{1260}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1476)+1476}{2*630}=\frac{2952}{1260}
=2+12/35
$