-9/7x+1/6=-8+5/8x

Solution for -9/7x+1/6=-8+5/8x equation:

-9/7x+1/6=-8+5/8x

We move all terms to the left:

-9/7x+1/6-(-8+5/8x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-9/7x-(5/8x-8)+1/6=0

We get rid of parentheses

-9/7x-5/8x+8+1/6=0

We calculate fractions


448x^2/2016x^2+(-2592x)/2016x^2+(-1260x)/2016x^2+8=0

We multiply all the terms by the denominator


448x^2+(-2592x)+(-1260x)+8*2016x^2=0

Wy multiply elements

448x^2+16128x^2+(-2592x)+(-1260x)=0

We get rid of parentheses

448x^2+16128x^2-2592x-1260x=0

We add all the numbers together, and all the variables

16576x^2-3852x=0

a = 16576; b = -3852; c = 0;
Δ = b2-4ac
Δ = -38522-4·16576·0
Δ = 14837904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14837904}=3852$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3852)-3852}{2*16576}=\frac{0}{33152}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3852)+3852}{2*16576}=\frac{7704}{33152}
=963/4144
$