8x-3/3x=5

Solution for 8x-3/3x=5 equation:

8x-3/3x=5

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


8x*3x-5*3x-3=0

Wy multiply elements

24x^2-15x-3=0

a = 24; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·24·(-3)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{57}}{2*24}=\frac{15-3\sqrt{57}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{57}}{2*24}=\frac{15+3\sqrt{57}}{48}
$