8x-3/3x=12

Solution for 8x-3/3x=12 equation:

8x-3/3x=12

We move all terms to the left:

8x-3/3x-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


8x*3x-12*3x-3=0

Wy multiply elements

24x^2-36x-3=0

a = 24; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·24·(-3)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{11}}{2*24}=\frac{36-12\sqrt{11}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{11}}{2*24}=\frac{36+12\sqrt{11}}{48}
$