8x+5=(10/3x)-2

Solution for 8x+5=(10/3x)-2 equation:

8x+5=(10/3x)-2

We move all terms to the left:

8x+5-((10/3x)-2)=0


Domain of the equation: 3x)-2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-((+10/3x)-2)+5=0

We multiply all the terms by the denominator


8x*3x)-2)-((+5*3x)-2)+10=0

Wy multiply elements

24x^2+15x=0

a = 24; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·24·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*24}=\frac{-30}{48}
=-5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*24}=\frac{0}{48}
=0
$