8/3x+5/2=-5/4x-19

Solution for 8/3x+5/2=-5/4x-19 equation:

8/3x+5/2=-5/4x-19

We move all terms to the left:

8/3x+5/2-(-5/4x-19)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-19)!=0

x∈R


We get rid of parentheses

8/3x+5/4x+19+5/2=0

We calculate fractions


240x^2/48x^2+128x/48x^2+60x/48x^2+19=0

We multiply all the terms by the denominator


240x^2+128x+60x+19*48x^2=0

We add all the numbers together, and all the variables

240x^2+188x+19*48x^2=0

Wy multiply elements

240x^2+912x^2+188x=0

We add all the numbers together, and all the variables

1152x^2+188x=0

a = 1152; b = 188; c = 0;
Δ = b2-4ac
Δ = 1882-4·1152·0
Δ = 35344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35344}=188$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(188)-188}{2*1152}=\frac{-376}{2304}
=-47/288
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(188)+188}{2*1152}=\frac{0}{2304}
=0
$