x-14/2x=4

Solution for x-14/2x=4 equation:

x-14/2x=4

We move all terms to the left:

x-14/2x-(4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-4*2x-14=0

Wy multiply elements

2x^2-8x-14=0

a = 2; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·2·(-14)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{11}}{2*2}=\frac{8-4\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{11}}{2*2}=\frac{8+4\sqrt{11}}{4}
$