1/8x-1/7x=10

Solution for 1/8x-1/7x=10 equation:

1/8x-1/7x=10

We move all terms to the left:

1/8x-1/7x-(10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


7x/56x^2+(-8x)/56x^2-10=0

We multiply all the terms by the denominator


7x+(-8x)-10*56x^2=0

Wy multiply elements

-560x^2+7x+(-8x)=0

We get rid of parentheses

-560x^2+7x-8x=0

We add all the numbers together, and all the variables

-560x^2-1x=0

a = -560; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-560)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-560}=\frac{0}{-1120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-560}=\frac{2}{-1120}
=-1/560
$