5x-2/2x=4

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

5x-2/2x=4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-8x-2=0

a = 10; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·10·(-2)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*10}=\frac{-4}{20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*10}=\frac{20}{20}
=1
$