5/8x+1/6x=-9

Solution for 5/8x+1/6x=-9 equation:

5/8x+1/6x=-9

We move all terms to the left:

5/8x+1/6x-(-9)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x+1/6x+9=0

We calculate fractions


30x/48x^2+8x/48x^2+9=0

We multiply all the terms by the denominator


30x+8x+9*48x^2=0

We add all the numbers together, and all the variables

38x+9*48x^2=0

Wy multiply elements

432x^2+38x=0

a = 432; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·432·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*432}=\frac{-76}{864}
=-19/216
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*432}=\frac{0}{864}
=0
$