8x-3/3x=2/1

Solution for 8x-3/3x=2/1 equation:

8x-3/3x=2/1

We move all terms to the left:

8x-3/3x-(2/1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

8x-3/3x-0=0

We add all the numbers together, and all the variables

8x-3/3x=0

We multiply all the terms by the denominator


8x*3x-3=0

Wy multiply elements

24x^2-3=0

a = 24; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·24·(-3)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*24}=\frac{0-12\sqrt{2}}{48}
=-\frac{12\sqrt{2}}{48}
=-\frac{\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*24}=\frac{0+12\sqrt{2}}{48}
=\frac{12\sqrt{2}}{48}
=\frac{\sqrt{2}}{4}
$