7x-1/2x=3

Solution for 7x-1/2x=3 equation:

7x-1/2x=3

We move all terms to the left:

7x-1/2x-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


7x*2x-3*2x-1=0

Wy multiply elements

14x^2-6x-1=0

a = 14; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·14·(-1)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*14}=\frac{6-2\sqrt{23}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*14}=\frac{6+2\sqrt{23}}{28}
$