4x-2/2x=7

Solution for 4x-2/2x=7 equation:

4x-2/2x=7

We move all terms to the left:

4x-2/2x-(7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-7*2x-2=0

Wy multiply elements

8x^2-14x-2=0

a = 8; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·8·(-2)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*8}=\frac{14-2\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*8}=\frac{14+2\sqrt{65}}{16}
$