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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

We get rid of parentheses

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

We calculate fractions


8x/24x^2+9x/24x^2+13+2=0

We add all the numbers together, and all the variables

8x/24x^2+9x/24x^2+15=0

We multiply all the terms by the denominator


8x+9x+15*24x^2=0

We add all the numbers together, and all the variables

17x+15*24x^2=0

Wy multiply elements

360x^2+17x=0

a = 360; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·360·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*360}=\frac{-34}{720}
=-17/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*360}=\frac{0}{720}
=0
$