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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: x+9)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


x/8x^2+(-48x)/8x^2-9+7=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2+x+(-48x)=0

We get rid of parentheses

-16x^2+x-48x=0

We add all the numbers together, and all the variables

-16x^2-47x=0

a = -16; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·(-16)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*-16}=\frac{94}{-32}
=-2+15/16
$