1/8x+1/8=1/7x-1

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

1/8x+1/8=1/7x-1

We move all terms to the left:

1/8x+1/8-(1/7x-1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 7x-1)!=0

x∈R


We get rid of parentheses

1/8x-1/7x+1+1/8=0

We calculate fractions


7x/3584x^2+(-512x)/3584x^2+7x/3584x^2+1=0

We multiply all the terms by the denominator


7x+(-512x)+7x+1*3584x^2=0

We add all the numbers together, and all the variables

14x+(-512x)+1*3584x^2=0

Wy multiply elements

3584x^2+14x+(-512x)=0

We get rid of parentheses

3584x^2+14x-512x=0

We add all the numbers together, and all the variables

3584x^2-498x=0

a = 3584; b = -498; c = 0;
Δ = b2-4ac
Δ = -4982-4·3584·0
Δ = 248004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{248004}=498$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-498)-498}{2*3584}=\frac{0}{7168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-498)+498}{2*3584}=\frac{996}{7168}
=249/1792
$