-5/8x-7/24x+1/3=42

Solution for -5/8x-7/24x+1/3=42 equation:

-5/8x-7/24x+1/3=42

We move all terms to the left:

-5/8x-7/24x+1/3-(42)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


determiningTheFunctionDomain
-5/8x-7/24x-42+1/3=0

We calculate fractions


384x^2/1728x^2+(-1080x)/1728x^2+(-504x)/1728x^2-42=0

We multiply all the terms by the denominator


384x^2+(-1080x)+(-504x)-42*1728x^2=0

Wy multiply elements

384x^2-72576x^2+(-1080x)+(-504x)=0

We get rid of parentheses

384x^2-72576x^2-1080x-504x=0

We add all the numbers together, and all the variables

-72192x^2-1584x=0

a = -72192; b = -1584; c = 0;
Δ = b2-4ac
Δ = -15842-4·(-72192)·0
Δ = 2509056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2509056}=1584$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1584)-1584}{2*-72192}=\frac{0}{-144384}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1584)+1584}{2*-72192}=\frac{3168}{-144384}
=-33/1504
$