x(7/2x)=14

Solution for x(7/2x)=14 equation:

x(7/2x)=14

We move all terms to the left:

x(7/2x)-(14)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+7/2x)-14=0

We multiply parentheses

7x^2-14=0

a = 7; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·7·(-14)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*7}=\frac{0-14\sqrt{2}}{14}
=-\frac{14\sqrt{2}}{14}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*7}=\frac{0+14\sqrt{2}}{14}
=\frac{14\sqrt{2}}{14}
=\sqrt{2}
$