5x-4/2x=2

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

5x-4/2x=2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-4x-4=0

a = 10; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·10·(-4)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*10}=\frac{4-4\sqrt{11}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*10}=\frac{4+4\sqrt{11}}{20}
$