3x-1/5x-4=0

Solution for 3x-1/5x-4=0 equation:

3x-1/5x-4=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


3x*5x-4*5x-1=0

Wy multiply elements

15x^2-20x-1=0

a = 15; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·15·(-1)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{115}}{2*15}=\frac{20-2\sqrt{115}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{115}}{2*15}=\frac{20+2\sqrt{115}}{30}
$