5/8x+1/3x=6

Solution for 5/8x+1/3x=6 equation:

5/8x+1/3x=6

We move all terms to the left:

5/8x+1/3x-(6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x/24x^2+8x/24x^2-6=0

We multiply all the terms by the denominator


15x+8x-6*24x^2=0

We add all the numbers together, and all the variables

23x-6*24x^2=0

Wy multiply elements

-144x^2+23x=0

a = -144; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-144)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-144}=\frac{-46}{-288}
=23/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-144}=\frac{0}{-288}
=0
$