(1/3x)+(5/8x)=-46

Solution for (1/3x)+(5/8x)=-46 equation:

(1/3x)+(5/8x)=-46

We move all terms to the left:

(1/3x)+(5/8x)-(-46)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3x)+(+5/8x)-(-46)=0

We add all the numbers together, and all the variables

(+1/3x)+(+5/8x)+46=0

We get rid of parentheses

1/3x+5/8x+46=0

We calculate fractions


8x/24x^2+15x/24x^2+46=0

We multiply all the terms by the denominator


8x+15x+46*24x^2=0

We add all the numbers together, and all the variables

23x+46*24x^2=0

Wy multiply elements

1104x^2+23x=0

a = 1104; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·1104·0
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*1104}=\frac{-46}{2208}
=-1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*1104}=\frac{0}{2208}
=0
$