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∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

24x^2+6x+15x-10=0

We add all the numbers together, and all the variables

24x^2+21x-10=0

a = 24; b = 21; c = -10;
Δ = b2-4ac
Δ = 212-4·24·(-10)
Δ = 1401
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{-(21)-\sqrt{1401}}{2*24}=\frac{-21-\sqrt{1401}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{1401}}{2*24}=\frac{-21+\sqrt{1401}}{48}
$