2x+1/7x=4

Solution for 2x+1/7x=4 equation:

2x+1/7x=4

We move all terms to the left:

2x+1/7x-(4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


2x*7x-4*7x+1=0

Wy multiply elements

14x^2-28x+1=0

a = 14; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·14·1
Δ = 728
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:

$\sqrt{\Delta}=\sqrt{728}=\sqrt{4*182}=\sqrt{4}*\sqrt{182}=2\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{182}}{2*14}=\frac{28-2\sqrt{182}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{182}}{2*14}=\frac{28+2\sqrt{182}}{28}
$