-1/7x+5/6x=9

Solution for -1/7x+5/6x=9 equation:

-1/7x+5/6x=9

We move all terms to the left:

-1/7x+5/6x-(9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


(-6x)/42x^2+35x/42x^2-9=0

We multiply all the terms by the denominator


(-6x)+35x-9*42x^2=0

We add all the numbers together, and all the variables

35x+(-6x)-9*42x^2=0

Wy multiply elements

-378x^2+35x+(-6x)=0

We get rid of parentheses

-378x^2+35x-6x=0

We add all the numbers together, and all the variables

-378x^2+29x=0

a = -378; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-378)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-378}=\frac{-58}{-756}
=29/378
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-378}=\frac{0}{-756}
=0
$