5/8x+1/3x=42

Solution for 5/8x+1/3x=42 equation:

5/8x+1/3x=42

We move all terms to the left:

5/8x+1/3x-(42)=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^2-42=0

We multiply all the terms by the denominator


15x+8x-42*24x^2=0

We add all the numbers together, and all the variables

23x-42*24x^2=0

Wy multiply elements

-1008x^2+23x=0

a = -1008; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-1008)·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*-1008}=\frac{-46}{-2016}
=23/1008
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-1008}=\frac{0}{-2016}
=0
$