3x-5=-8(6/5x)

Solution for 3x-5=-8(6/5x) equation:

3x-5=-8(6/5x)

We move all terms to the left:

3x-5-(-8(6/5x))=0


Domain of the equation: 5x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-8(+6/5x))-5=0

We multiply all the terms by the denominator


3x*5x))-(-8(-5*5x))+6=0

Wy multiply elements

15x^2-25x=0

a = 15; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·15·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*15}=\frac{50}{30}
=1+2/3
$