5x-3=2/4x

Solution for 5x-3=2/4x equation:

5x-3=2/4x

We move all terms to the left:

5x-3-(2/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+2/4x)-3=0

We get rid of parentheses

5x-2/4x-3=0

We multiply all the terms by the denominator


5x*4x-3*4x-2=0

Wy multiply elements

20x^2-12x-2=0

a = 20; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·20·(-2)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{19}}{2*20}=\frac{12-4\sqrt{19}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{19}}{2*20}=\frac{12+4\sqrt{19}}{40}
$