8x-5/3x-5=3

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

8x-5/3x-5=3

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

24x^2-24x-5=0

a = 24; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·24·(-5)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{66}}{2*24}=\frac{24-4\sqrt{66}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{66}}{2*24}=\frac{24+4\sqrt{66}}{48}
$