2/3x-5=5x+8

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

2/3x-5=5x+8

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-5x*3x-8*3x-5*3x+2=0

Wy multiply elements

-15x^2-24x-15x+2=0

We add all the numbers together, and all the variables

-15x^2-39x+2=0

a = -15; b = -39; c = +2;
Δ = b2-4ac
Δ = -392-4·(-15)·2
Δ = 1641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1641}}{2*-15}=\frac{39-\sqrt{1641}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1641}}{2*-15}=\frac{39+\sqrt{1641}}{-30}
$