53x-4/3x-1=8

Solution for 53x-4/3x-1=8 equation:

53x-4/3x-1=8

We move all terms to the left:

53x-4/3x-1-(8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

53x-4/3x-9=0

We multiply all the terms by the denominator


53x*3x-9*3x-4=0

Wy multiply elements

159x^2-27x-4=0

a = 159; b = -27; c = -4;
Δ = b2-4ac
Δ = -272-4·159·(-4)
Δ = 3273
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{-(-27)-\sqrt{3273}}{2*159}=\frac{27-\sqrt{3273}}{318}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{3273}}{2*159}=\frac{27+\sqrt{3273}}{318}
$