(8/3x)-(1/2x)=-13

Solution for (8/3x)-(1/2x)=-13 equation:

(8/3x)-(1/2x)=-13

We move all terms to the left:

(8/3x)-(1/2x)-(-13)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/3x)-(+1/2x)-(-13)=0

We add all the numbers together, and all the variables

(+8/3x)-(+1/2x)+13=0

We get rid of parentheses

8/3x-1/2x+13=0

We calculate fractions


16x/6x^2+(-3x)/6x^2+13=0

We multiply all the terms by the denominator


16x+(-3x)+13*6x^2=0

Wy multiply elements

78x^2+16x+(-3x)=0

We get rid of parentheses

78x^2+16x-3x=0

We add all the numbers together, and all the variables

78x^2+13x=0

a = 78; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·78·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*78}=\frac{-26}{156}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*78}=\frac{0}{156}
=0
$