9/x+6=5/6x+8

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

9/x+6=5/6x+8

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


54x/6x^2+(-5x)/6x^2-8+6=0

We add all the numbers together, and all the variables

54x/6x^2+(-5x)/6x^2-2=0

We multiply all the terms by the denominator


54x+(-5x)-2*6x^2=0

Wy multiply elements

-12x^2+54x+(-5x)=0

We get rid of parentheses

-12x^2+54x-5x=0

We add all the numbers together, and all the variables

-12x^2+49x=0

a = -12; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-12)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-12}=\frac{-98}{-24}
=4+1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-12}=\frac{0}{-24}
=0
$