-3/2x-5=2/3x+8

Solution for -3/2x-5=2/3x+8 equation:

-3/2x-5=2/3x+8

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

-3/2x-2/3x-8-5=0

We calculate fractions


(-9x)/6x^2+(-4x)/6x^2-8-5=0

We add all the numbers together, and all the variables

(-9x)/6x^2+(-4x)/6x^2-13=0

We multiply all the terms by the denominator


(-9x)+(-4x)-13*6x^2=0

Wy multiply elements

-78x^2+(-9x)+(-4x)=0

We get rid of parentheses

-78x^2-9x-4x=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{0}{-156}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-78}=\frac{26}{-156}
=-1/6
$