7x-1/2x=0

Solution for 7x-1/2x=0 equation:

7x-1/2x=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


7x*2x-1=0

Wy multiply elements

14x^2-1=0

a = 14; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·14·(-1)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*14}=\frac{0-2\sqrt{14}}{28}
=-\frac{2\sqrt{14}}{28}
=-\frac{\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*14}=\frac{0+2\sqrt{14}}{28}
=\frac{2\sqrt{14}}{28}
=\frac{\sqrt{14}}{14}
$