1/8x-5=1/6x+10

Solution for 1/8x-5=1/6x+10 equation:

1/8x-5=1/6x+10

We move all terms to the left:

1/8x-5-(1/6x+10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 6x+10)!=0

x∈R


We get rid of parentheses

1/8x-1/6x-10-5=0

We calculate fractions


6x/48x^2+(-8x)/48x^2-10-5=0

We add all the numbers together, and all the variables

6x/48x^2+(-8x)/48x^2-15=0

We multiply all the terms by the denominator


6x+(-8x)-15*48x^2=0

Wy multiply elements

-720x^2+6x+(-8x)=0

We get rid of parentheses

-720x^2+6x-8x=0

We add all the numbers together, and all the variables

-720x^2-2x=0

a = -720; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-720)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-720}=\frac{0}{-1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-720}=\frac{4}{-1440}
=-1/360
$