x(1/2x)=34

Solution for x(1/2x)=34 equation:

x(1/2x)=34

We move all terms to the left:

x(1/2x)-(34)=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(+1/2x)-34=0

We multiply parentheses

x^2-34=0

a = 1; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·1·(-34)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{34}}{2*1}=\frac{0-2\sqrt{34}}{2}
=-\frac{2\sqrt{34}}{2}
=-\sqrt{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{34}}{2*1}=\frac{0+2\sqrt{34}}{2}
=\frac{2\sqrt{34}}{2}
=\sqrt{34}
$