5*2x=14/x

Solution for 5*2x=14/x equation:

5*2x=14/x

We move all terms to the left:

5*2x-(14/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5*2x-(+14/x)=0

Wy multiply elements

10x-(+14/x)=0

We get rid of parentheses

10x-14/x=0

We multiply all the terms by the denominator


10x*x-14=0

Wy multiply elements

10x^2-14=0

a = 10; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·10·(-14)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*10}=\frac{0-4\sqrt{35}}{20}
=-\frac{4\sqrt{35}}{20}
=-\frac{\sqrt{35}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*10}=\frac{0+4\sqrt{35}}{20}
=\frac{4\sqrt{35}}{20}
=\frac{\sqrt{35}}{5}
$